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Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Linear derivation; linear n-derivation; generalized linear n-derivation; Lie ideal; Banach algebra; C*-algebra

Online: 10 April 2024 (10:09:03 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202110.0087.v22

On the Additive and Subtractive Representation of Even Numbers from Primes

Ali Shehu, Jetmira Uka

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: sieve of eratosthenes; goldbach conjecture; polignac conjecture; twin prime conjecture

Online: 4 April 2024 (17:39:40 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202404.0268.v1

Covers of Finitely Generated Acts over Monoids

Xiaoqin Zhang, Tingting Zhao

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: cover; coproduct; finitely generated; $\mathcal{X}$-precover

Online: 3 April 2024 (08:28:04 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202403.1718.v1

Prime Factorization and Diophantine Quintic Equations Insights, Challenges, and New Directions

Budee U Zaman

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: algebraic methods,quintic problem,Diophantine equation ,prime number

Online: 28 March 2024 (09:35:31 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.0963.v1

The Generalized Eta Transformation Formulas as the Hecke Modular Relation

Nianliang Wang, Takato kuzumaki, Shigeru Kanemitsu

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: RHB correspondence; transformation formula for Lambert series; Hurwitz zeta-function; Lerch zeta-function; vector space structure

Online: 18 March 2024 (08:12:55 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.0664.v1

The Jacobian Conjecture and Idempotent Ideals

Lukasz Matysiak

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: automorphism; idempotent ideal; Jacobian conjecture; polynomial mapping

Online: 12 March 2024 (13:46:14 CET)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v30

A Proof of the Riemann Hypothesis Based on a New Expression of the Completed Zeta Function

Weicun Zhang

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann Hypothesis (RH); proof; completed zeta function

Online: 8 March 2024 (15:56:30 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.1638.v1

Prime Solutions to the Diophantine Equation 2ⁿ = p² +7

Budee U Zaman

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: integers; ; Diophantine Equation; prime number

Online: 28 February 2024 (13:55:57 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.1484.v1

(m, n)-Closed Submodules of Modules over Commutative Rings

Ece Yetkin Celikel, Hani Khashan

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: (m,n)-closed ideals, (m,n)-prime ideals, (m,n)-closed submodules, n-absorbing submodules

Online: 26 February 2024 (15:33:56 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.1143.v1

Finite and Symmetric Euler Sums and Multiple T-Values

Jianqiang Zhao

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: (finite) Euler sums; symmetric Euler sums; (finite) multiple T-values; symmetric multiple T-values; alternating multiple T-values

Online: 20 February 2024 (14:34:09 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.1108.v1

Exploring the Connection between Prime Numbers, Trigonometric Functions, and the Riemann Hypothesis through ln(sec(π.nlog(n)))

Budee U Zaman

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: prime numbers; Riemann Hypothesis; analytic functions; trigonometric functions

Online: 20 February 2024 (08:49:02 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.1003.v1

On Certain Properties of Square-Free Numbers and the Function s(n)

Lukasz Matysiak, Julia Fidler

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: monoid; Riemann hypothesis; square-free factorization; square-free number

Online: 19 February 2024 (07:58:05 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.0910.v1

On Generalized Fibospinomials: Generalized Fibonacci Polynomial Spinors

Ece Gulsah Colak, Nazmiye Gonul Bilgin, Yuksel Soykan

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: fibonacci numbers; fibonacci polynomials; fibonacci spinors; generalized fibonacci spinors; generalized fibonacci polynomial spinors

Online: 16 February 2024 (14:15:45 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.0842.v1

Exploring the Collatz Conjecture through Directed Graphs

Budee U Zaman

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Collatz Conjecture; Even Numbers; Odd Number; Directed Graphs

Online: 15 February 2024 (08:32:21 CET)

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Preprint ARTICLE | doi:10.20944/preprints202110.0087.v21

On the Additive and Subtractive Representation of Even Numbers from Primes

Ali Shehu, Jetmira Uka

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: sieve of eratosthenes; goldbach conjecture; polignac conjecture; twin prime conjecture

Online: 13 February 2024 (07:15:16 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.0673.v1

Validating Collatz Conjecture through Binary Representation and Probabilistic Path Analysis

Budee U Zaman

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: integer; Collatz conjecture; Binary number

Online: 12 February 2024 (10:48:10 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.0598.v1

Cohen-Macaulayness of Vertex Splittable Monomial Ideals

Marilena Crupi, Antonino Ficarra

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Cohen-Macaulay ideals; vertex splittable ideals

Online: 9 February 2024 (14:56:26 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.0588.v1

Gocgen Approach for Zeta Function in Twin Primes

Ahmet F. Gocgen

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: number theory, twin prime conjecture, gocgen approach, prime numbers, zeta function

Online: 9 February 2024 (11:57:30 CET)

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Preprint ARTICLE | doi:10.20944/preprints202110.0087.v20

On the Additive and Subtractive Representation of Even Numbers from Primes

Ali Shehu, Jetmira Uka, Ali Shehu

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: sieve of eratosthenes; goldbach conjecture; polignac conjecture; twin prime conjecture

Online: 9 February 2024 (11:19:03 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.0545.v1

Global Generalized Mersenne Numbers: Definition, Decomposition, and Generalized Theorems

Vladimir Pletser

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Mersenne numbers; Generalized Mersenne numbers; divisibility and congruence properties

Online: 9 February 2024 (10:50:56 CET)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v29

A Proof of the Riemann Hypothesis Based on a New Expression of the Completed Zeta Function

Weicun Zhang

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann Hypothesis (RH); proof; completed zeta function

Online: 6 February 2024 (11:07:21 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.0335.v1

The Germany Problem for Beal's Conjecture

Ahmet Gocgen

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: number theory, beals conjecture, germany problem, composite numbers

Online: 6 February 2024 (05:23:05 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.0238.v1

General Divisibility Algorithms

Can Kaan KAYA

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Arithmetic Functions; Discrete Mathematics; Primes; Number Theory

Online: 5 February 2024 (08:02:06 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.0051.v1

Meeting at Both Ends Information – Theoretic Semi-group Theory of Uncertain Reasoning

Ismail A. Mageed

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: ré; nyi generalized entropies (RGEs); information theory; semi-group theory; uncertain reasoning

Online: 1 February 2024 (12:51:14 CET)

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Preprint ARTICLE | doi:10.20944/preprints202401.1533.v1

Gocgen Approach for Bounded Gaps Between Odd Composite Numbers

Ahmet Gocgen

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: number theory; twin prime conjecture; gocgen approach; prime numbers

Online: 22 January 2024 (10:08:26 CET)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v28

A Proof of the Riemann Hypothesis Based on a New Expression of the Completed Zeta Function

Weicun Zhang

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann Hypothesis (RH); proof; completed zeta function

Online: 12 January 2024 (14:53:47 CET)

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Preprint ARTICLE | doi:10.20944/preprints202401.0472.v1

(m, n)-Prime Ideals of Commutative Rings

Hani Khashan, Ece Yetkin Celikel

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: (m; n)-prime ideal; (m; n)-closed ideal; n-absorbing ideal; avoidance theorem

Online: 5 January 2024 (14:21:25 CET)

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Preprint ARTICLE | doi:10.20944/preprints202401.0052.v1

Generalized Reynolds Operators on Hom-Lie Triple Systems

Yunpeng Xiao, Wen Teng, Fengshan Long

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Hom-Lie triple system; generalized Reynolds operator; cohomology; deformation; Hom-NS-Lie triple system

Online: 2 January 2024 (10:00:34 CET)

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Preprint ARTICLE | doi:10.20944/preprints202401.0068.v1

On the Sums over Inverse Powers of Zeroes of the Hurwitz Zeta-Function, and Some Related Properties of These Zeroes

Sekatski Serguei

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Logarithm of an analytical function; Generalized Littlewood theorem; Hurwitz zeta-function; zeroes and poles of analytical function

Online: 2 January 2024 (09:43:48 CET)

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Preprint ARTICLE | doi:10.20944/preprints202312.2327.v1

Linear Relations between Numbers of Terms and First Terms of Sums of Consecutive Squared Integers Equal to Squared Integers

Vladimir Pletser

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Sums of consecutive squared integers equal to square integers; Quadratic diophantine equation; Generalized Pell equation; Fundamental solutions; Chebyshev polynomials

Online: 29 December 2023 (15:30:23 CET)

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Preprint REVIEW | doi:10.20944/preprints202312.1878.v1

Automorphism Group of Polyhedral Graphs

Modjtaba Ghorbani, Razie Alidehi-Ravandi, Matthias Dehmer

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: symmetry; automorphism group; polyhedral graph; fullerene

Online: 25 December 2023 (15:57:27 CET)

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Preprint ARTICLE | doi:10.20944/preprints202312.1618.v1

Proof of the Riemann Hypothesis Using the Decomposition Zeta(s) = X(s) – Y(s)

Pedro Caceres

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: riemann hypothesis; prime numbers; infinite power series; number theory

Online: 21 December 2023 (08:06:19 CET)

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Prime numbers are the atoms of mathematics and mathematics is needed to make sense of the real world. Finding the Prime number structure and eventually being able to crack their code is the ultimate goal in what is called Number Theory. From the evolution of species to cryptography, Nature finds help in Prime numbers. One of the most important advances in the study of Prime numbers was the paper by Bernhard Riemann in November 1859 called “Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse” (On the number of primes less than a given quantity). In that paper, Riemann gave a formula for the number of primes less than x in terms the integral of 1/log(x) and the roots (zeros) of the zeta function defined by: Where ζ(z) is a function of a complex variable z that analytically continues the Dirichlet series. Riemann also formulated a conjecture about the location of the zeros of RZF, which fall into two classes: the "trivial zeros" -2, -4, -6, etc., and those whose real part lies between 0 and 1. Riemann's conjecture Riemann hypothesis [RH] was formulated as this: [RH] The real part of every nontrivial zero z* of the RZF is 1/2. Proving the RH is, as of today, one of the most important problems in mathematics. In this paper we will provide a proof of the RH. The proof of the RH will be built following these five parts: PART 1: Description of the RZF PART 2: The C-transformation PART 3: Application of the C-transformation to in Re(z) 0 to obtain ζ(z)=X(z)-Y(z) PART 4: Analysis of the values of z such that X(z)=Y(z), and |X(z)|=|Y(z)|, that equates to ζ(z)=0 Proof that |X(z)|=|Y(z)| only if Re(z)=1/2 Conclude that ζ(z)=0 only if Re(z)=1/2 for Re(z) 0 PART 5: We will also prove that all non-trivial zeros of ζ(z) in the critical line of the form are not distributed randomly. There is a relationship between the values of those zeros and the Harmonic function that leads to an algebraic relationship between any two zeros.

Preprint ARTICLE | doi:10.20944/preprints202312.1409.v1

C-S and Strongly C-S Orthogonal Matrices

Xiaoji Liu, Ying Liu, Hongwei Jin

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: C-S inverse; C-S orthogonality; Strongly C-S orthogonality; C-S additivity; C-S partial order

Online: 19 December 2023 (10:46:12 CET)

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Preprint TECHNICAL NOTE | doi:10.20944/preprints202312.1215.v1

On the Equality of ‘Stopping Times’ of Hailstone Numbers

Aditya Dalal

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Collatz Conjecture, Proof, Induction

Online: 18 December 2023 (07:18:11 CET)

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Preprint ARTICLE | doi:10.20944/preprints202312.0133.v1

Tangles with k Ropes and 2k Hands

Aashna Hari, Emma Li, Rachel Liu

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: tangles; isomorphism; analogs of groups; matrices; group presentation

Online: 4 December 2023 (04:16:55 CET)

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Preprint ARTICLE | doi:10.20944/preprints202309.1012.v3

A Necessary and Sufficient Condition for Proof of the Binary Goldbach Conjecture. Proofs of Binary Goldbach, Andrica and Legendre Conjectures. Notes on the Riemann Hypothesis. (Edition 8D)

Samuel Buya, John Bezaleel Nchima

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: proof of Binary Golbdach conjecture; proof of Andrica conjecture; proof of Legendre conjecture; Goldbach partition semiprime; disproof of Riemann hypothesis; proof of twin prime conjecture

Online: 30 November 2023 (05:11:18 CET)

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Preprint ARTICLE | doi:10.20944/preprints202311.1660.v1

Analyzing Twin Primes, Goldbach’s Strong Conjecture and Polignac’s Conjecture

Mercedes Orús-Lacort, Román Orús, Christophe Jouis

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Number Theory; Twin Primes; Goldbach’s Strong Conjecture; Polignac’s Conjecture

Online: 27 November 2023 (11:09:06 CET)

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Preprint ARTICLE | doi:10.20944/preprints202310.0485.v4

A Note on Invo-Regular Unital Rings

S K Pandey

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Boolean ring; unit regular ring; invo-regular ring; tripotent ring, quasi invo-regular ring, strongly invo-regular ring, weakly tripotent ring

Online: 8 November 2023 (09:53:50 CET)

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Preprint SHORT NOTE | doi:10.20944/preprints202310.0212.v3

Disproof of Several Recently Published Results in Ring Theory

S K Pandey

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: ring theory; algebra; mathematics; disproof; counterexamples; involution t-clean ring; weakly tripotent ring; invo-regular ring; locally invo-regular ring; strongly 2-nil clean ring; strongly nil clean ring

Online: 6 November 2023 (10:25:33 CET)

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Preprint ARTICLE | doi:10.20944/preprints202311.0284.v1

Fibonacci Identities via Calculus

Kunle Adegoke

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Fibonacci number, Lucas number, gibonacci sequence, generalized Fibonacci sequence, summation identity, Gelin-Ces\`aro identity, Candido's identity.

Online: 6 November 2023 (08:16:09 CET)

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Preprint SHORT NOTE | doi:10.20944/preprints202310.0212.v2

Disproof of Several Recently Published Results in Ring Theory

S K Pandey

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: ring theory; algebra; mathematics; disproof; counterexamples; involution t-clean ring, weakly tripotent ring

Online: 1 November 2023 (02:37:41 CET)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v27

A Proof of the Riemann Hypothesis Based on a New Expression of the Completed Zeta Function

Weicun Zhang

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann Hypothesis (RH); proof; completed zeta function

Online: 30 October 2023 (10:34:15 CET)

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Preprint ARTICLE | doi:10.20944/preprints202310.0485.v3

A Note on Invo-Regular Unital Rings

S K Pandey

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Boolean ring; unit regular ring; invo-regular ring; involution

Online: 26 October 2023 (11:32:25 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.1669.v1

Equalities for Mixed Operations of Moore–Penrose and Group Inverses of a Matrix

Yongge Tian

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: group inverse; matrix equality; Moore--Penrose inverse; range; rank

Online: 25 October 2023 (16:12:36 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.0968.v2

On Weakly Tripotent and Locally Invo-Regular Rings

S K Pandey

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: tripotent ring; weakly tripotent ring; locally invo-regular ring; involution t-clean ring

Online: 25 October 2023 (09:56:55 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.1091.v1

All Bi-Unitary Superperfect Polynomials over F2 with at Most Two Irreducible Factors

Haissam Chehade, Domoo Miari, Yousuf Alkhezi

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: sum of divisors; bi-unitary divisors; polynomials; finite fields; characteristic 2

Online: 17 October 2023 (11:59:49 CEST)

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Preprint HYPOTHESIS | doi:10.20944/preprints202310.1050.v1

A Potential Proof of Riemann Hypothesis

Miguel Seisdedos García

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: prime numbers; riemann hypothesis; zeta function; analytic continuation; zeros

Online: 17 October 2023 (08:30:27 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.0968.v1

On Weakly Tripotent and Locally Invo-Regular Rings

S K Pandey

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: tripotent ring; weakly tripotent ring; locally invo-regular rings

Online: 16 October 2023 (12:34:04 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v26

A Proof Of The Riemann Hypothesis Based On A New Expression Of The Completed Zeta Function

Weicun Zhang

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann Hypothesis (RH); proof; completed zeta function

Online: 16 October 2023 (08:31:26 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.0485.v2

A Note on Invo-Regular Unital Rings

S K Pandey

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Boolean ring; unit regular ring; invo-regular ring; involution

Online: 10 October 2023 (11:55:51 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.0485.v1

A Note on Invo-Regular Unital Rings

S K Pandey

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Boolean ring; unit regular ring; invo-regular ring; involution

Online: 9 October 2023 (11:07:57 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.0393.v1

Generalized EP elements in Banach *-algebras

Huanyin Chen, Marjan Sheibani

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: EP element; *-DMP element; generalized core-EP inverse; additive property; generalized core-EP order; Banach algebra.

Online: 9 October 2023 (08:09:37 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.1012.v2

A Necessary and Sufficient Condition for Proof of the Binary Goldbach Conjecture. Proofs of Binary Goldbach, Andrica and Legendre Conjectures. Notes on the Riemann Hypothesis. (Edition 8D)

Samuel Buya, John Bezaleel Nchima

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: proof of Binary Golbdach conjecture; proof of Andrica conjecture; proof of Legendre conjecture; Goldbach partition semiprime; disproof of Riemann hypothesis; proof of twin prime conjecture

Online: 7 October 2023 (08:13:27 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.0219.v1

Weighted Generalized Group Inverse in Banach *-Algebras

Huanyin Chen, Marjan Sheibani

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: generalized core-EP inverse; generalized group inverse; weighted generalized Drazin inverse; weighted weak group inverse; Banach *-algebra

Online: 4 October 2023 (07:21:50 CEST)

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Preprint SHORT NOTE | doi:10.20944/preprints202310.0212.v1

Disproof of Several Recently Published Results in Ring Theory

S K Pandey

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: ring theory; algebra; mathematics; disproof; counterexamples

Online: 4 October 2023 (05:28:47 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.2161.v2

A Proof of Collatz Conjecture

HUANG Qingxue

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: number theory; Collatz conjecture

Online: 22 September 2023 (07:42:19 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.1200.v1

Proof the Collatz Conjecture by a new view of natural numbers

Jishe Feng

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: binary representation; composite function; Collatz conjecture; ultimately periodic sequence; chaos

Online: 19 September 2023 (08:07:22 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.1012.v1

A necessary and sufficient condition for proof of the Binary Goldbach conjecture. Proofs of Binary Goldbach, Andrica and Legendre conjectures. Notes on the Riemann hypothesis. (Edition 8D)

Samuel Buya, John Bezaleel Nchima

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Proof of Binary Golbdach conjecture; Proof of Andrica conjecture; Proof of Legendre conjecture; Goldbach partition semiprime; Disproof of Riemann hypothesis

Online: 15 September 2023 (04:23:12 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.0723.v1

On the Order Estimate of the Mertens Function and its Relation to the Zeros of the Riemann Zeta Function

Subham De

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: arithmetic function; Mo¨bius function; Riemann Zeta function; Mertens function; Redheffer Matrix; Riemann Hypothesis; Roesler Matrix; spectral radius; Mertens Hypothesis

Online: 12 September 2023 (08:55:16 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.0481.v1

On Index Divisors and Monogenity of Certain Number Fields Defined by Trinomials x⁷+ax+b

Lhoussain El Fadil

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Power integral bases; theorem of Ore; prime ideal factorization; common index divisor

Online: 7 September 2023 (07:08:03 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202210.0432.v4

Proof of the Collatz Conjecture

Bülent Sukuşu

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Collatz operation; Collatz inverse operation; Collatz numbers

Online: 6 September 2023 (10:27:26 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.0320.v1

The Structure of Semiconic Idempotent Commutative Residuated Lattices

Wei Chen

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Residuated lattices; Idempotent semigroup; Chain; Construction; Amalgamation

Online: 6 September 2023 (05:27:17 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202212.0171.v2

Proof of Two-dimensional Jacobian Conjecture

Yucai Su

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Jacobian conjecture; Keller maps; injectivity of Keller maps

Online: 6 September 2023 (03:33:44 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202308.0928.v1

On Symmetric Generalized n-Derivations on Prime Ideals

Turki Alsuraiheed, Shakir Ali, Vaishali Varshney, Indah Emilia Wijayanti

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Prime ring; prime ideal; derivation; symmetric n-derivation; symmetric generalized n-derivation

Online: 11 August 2023 (09:53:22 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202110.0087.v19

On the Additive and Subtractive Representation of Even Numbers from Primes

Ali Shehu, Jetmira Uka

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: sieve of eratosthenes; goldbach conjecture; polignac conjecture; twin prime conjecture

Online: 10 August 2023 (05:23:00 CEST)

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Preprint COMMUNICATION | doi:10.20944/preprints202308.0106.v1

Is It Worth Testing Large Numbers for Collatz Conjecture?

Gaurav Goyal

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Collatz conjecture; 3n+1 problem; inequality relations

Online: 2 August 2023 (08:01:29 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202307.1834.v2

An Algebraic Proof of the Jacobian Conjecture

Qianghui Xiao

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Jacobian Conjecture, 3-fold linear type map, General 3-fold linear type map, Homogeneous type map, Jacobian condition, Coordinate transformation, Equivalent algebraic equations, Invariance of the Jacobian condition, General chain expression, Inverse polynomial map, Injective problem

Online: 1 August 2023 (09:46:21 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202307.1834.v1

An Algebraic Proof of the Jacobian Conjecture

Qianghui Xiao

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Jacobian Conjecture; 3-fold linear type map; Jacobian condition; Coordinate transformation; Equivalent algebraic equations; General chain expression

Online: 27 July 2023 (09:41:03 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202110.0087.v18

On the Additive and Subtractive Representation of Even Numbers from Primes

Ali Shehu, Jetmira Uka

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Sieve of Eratosthenes; Goldbach conjecture; Polignac conjecture; Twin Prime conjecture

Online: 13 July 2023 (10:01:00 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202307.0401.v1

Addition Formula of the Theta Function and Square Sums Theorem

Hong Cun Zhai

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Theta function; Weierstrass Sigma function; Weierstrass Elliptic function; Square sums 5 theorem

Online: 6 July 2023 (08:50:25 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202307.0252.v1

On Certain Modular Equations of Degree Three

Hong-Cun Zhai

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Ramanujan's theta function; Modular equation; $q$-Shifted factorial

Online: 5 July 2023 (03:39:26 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202306.1164.v6

On the Constant Terms of Certain Laurent Series

Barry Brent

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Laurent series; constant term; modular form; integer partition

Online: 29 June 2023 (02:07:30 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202306.1164.v5

On the Constant Terms of Certain Laurent Series

Barry Brent

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Laurent series; constant term; modular form; integer partition

Online: 26 June 2023 (05:23:28 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202306.1164.v4

On the Constant Terms of Certain Laurent Series

Barry Brent

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Laurent series; constant term; modular form; integer partition

Online: 21 June 2023 (02:46:26 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202306.1164.v3

On the Constant Terms of Certain Laurent Series

Barry Brent

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Laurent series; constant term; modular form; integer partition

Online: 20 June 2023 (02:58:25 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202306.1164.v2

On the Constant Terms of Certain Laurent Series

Barry Brent

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Laurent series; constant term; modular form; integer partition

Online: 19 June 2023 (05:14:08 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202306.1164.v1

On the Constant Terms of Certain Laurent Series

Barry Brent

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Laurent series; constant term; modular form; integer partition

Online: 16 June 2023 (03:45:35 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202306.0163.v1

Posner’s Theorem and *-Centralizing Derivations on Prime Ideals with Applications

Shakir Ali, Turki M. Alsuraiheed, Mohammad Salahuddin Khan, Cihat Abdioglu, Mohammed Ayedh, Naira N. Rafique

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Derivation; *-centralizing derivation; *-commuting derivation; involution; prime ideal; prime ring; semiprime ring

Online: 2 June 2023 (08:59:17 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.0931.v2

Proof the Collatz Conjecture in Binary Strings

Jishe Feng

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Collatz conjecture; binary number; ultimately periodic; chaos

Online: 19 May 2023 (16:16:49 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202303.0420.v7

A Common Approach to Three Open Problems in Number Theory

Apoloniusz Tyszka

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Brocard's problem; Brocard-Ramanujan equation x!+1=y^2; composite Fermat numbers; composite numbers of the form 2^(2^n)+1; Erd\"os' equation x(x+1)=y!

Online: 18 May 2023 (08:25:27 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.1118.v1

The Recursive Structures of Manin Symbols over $\mathbb{Q}$, Cusps and Elliptic Points on $X_0(N)$

SanMin Wang

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: modular curve; elliptic curve; recursive structure; Manin's symbols over $\mathbb{Q}$; cusps; elliptical points; algorithmic number theory

Online: 16 May 2023 (07:23:25 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.0905.v1

Transposed Poisson Superalgebra

Viktor Abramov, Olga Liivapuu

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Commutative superalgebra; Lie superalgebra, Poisson algebra; transposed Poisson algebra; graded differential algebra; quantum Yang-Mills theory

Online: 12 May 2023 (08:38:03 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202303.0420.v6

A Common Approach to Three Open Problems in Number Theory

Apoloniusz Tyszka

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Brocard's problem; Brocard-Ramanujan equation x!+1=y^2; composite Fermat numbers; composite numbers of the form 2^(2^n)+1; Erd\"os' equation x(x+1)=y!

Online: 11 May 2023 (04:42:23 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.1241.v3

Closed Form Solution to the Roots of a Quadratic Equation over the Quaternions

Edward King Solomon

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Quaternion; Quadratic Equation; Roots

Online: 9 May 2023 (04:36:31 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.0093.v6

Resolution of the 3n+1 Problem Using Inequality Relation Between Indices of 2 and 3

Gaurav Goyal

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Collatz conjecture; 3n+1; inequality relations

Online: 9 May 2023 (04:15:37 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.1241.v2

The Quadratic Equation for the Quaternions: The Closed Form Solution

Edward King Solomon

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Quaternion; Quadratic Equation; Roots

Online: 6 May 2023 (04:13:34 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.0093.v5

Resolution of the 3n+1 Problem Using Inequality Relation Between Indices of 2 and 3

Gaurav Goyal

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Collatz conjecture; 3n+1; inequality relations

Online: 5 May 2023 (10:18:23 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.0071.v1

Does the Collatz Sequence Eventually Reach 1 for All Positive Integer Initial Values?

Masoud Allame, Abdollah Hadi-Vencheh

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Collatz Conjecture; 3x + 1 Conjecture; base-2 numeral system

Online: 2 May 2023 (08:10:49 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.1241.v1

The Quadratic Equation for the Quaternions: The Closed Form Solution

Edward King Solomon

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Quaternion; Quadratic Equation; Roots

Online: 30 April 2023 (02:43:13 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202303.0420.v5

A Common Approach to Three Open Problems in Number Theory

Apoloniusz Tyszka

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Brocard's problem; Brocard-Ramanujan equation x!+1=y^2; composite Fermat numbers; composite numbers of the form 2^(2^n)+1; Erd\"os' equation x(x+1)=y!

Online: 27 April 2023 (04:44:46 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.0931.v1

Proof the Collatz Conjecture in Binary Strings

Jishe Feng

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Collatz conjecture; binary number; ultimately periodic; chaos

Online: 26 April 2023 (03:01:31 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.0093.v4

Resolution of the 3n+1 Problem Using Inequality Relation Between Indices of 2 and 3

Gaurav Goyal

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Collatz conjecture; 3n+1; inequality relations

Online: 21 April 2023 (09:25:33 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202303.0420.v4

A Common Approach to Three Open Problems in Number Theory

Apoloniusz Tyszka

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Brocard's problem; Brocard-Ramanujan equation x!+1=y^2; composite Fermat numbers; composite numbers of the form 2^(2^n)+1; Erd\"os' equation x(x+1)=y!

Online: 19 April 2023 (05:34:48 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v25

A Proof Of The Riemann Hypothesis Based On A New Expression Of The Completed Zeta Function

Weicun Zhang

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function

Online: 17 April 2023 (04:41:40 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202303.0420.v3

A Common Approach to Three Open Problems in Number Theory

Apoloniusz Tyszka

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Brocard's problem; Brocard-Ramanujan equation x!+1=y^2; composite Fermat numbers; composite numbers of the form 2^(2^n)+1; Erd\"os' equation x(x+1)=y!

Online: 17 April 2023 (04:05:43 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.0093.v3

Resolution of the 3n+1 Problem Using Inequality Relation Between Indices of 2 and 3

Gaurav Goyal

Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Collatz conjecture; 3n+1; inequality relations

Online: 11 April 2023 (10:05:24 CEST)

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Collatz conjecture states that an integer n reduces to 1 when certain simple operations are applied to it. Mathematically, the Collatz function is written as .

f^{k} (n) = \frac{3^{k} n + C}{2^{z}}

, where z, k, C

\geq

1.Suppose the integer n violates Collatz conjecture by reappearing, then the equation modifies to

n = \frac{3^{k}}{2^{z}} n + \frac{C}{2^{z}}

. The article takes an elementary approach to this problem by calculating the maximum value of

\frac{C}{2^{Z}}

. Correspondingly, an upper limit on the integer n is placed that re-appears in the sequence. The limit is found to be

n < 3.5

. Next, it shown that the integer n repeats in the sequence if

n < 0

. Finally, it is shown that no integer chain exists that does not lead to 1.

Computer Science and Mathematics