Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Analyzing Collatz Conjecture Using the Mathematical Complete Induction Method

Version 1 : Received: 11 May 2022 / Approved: 13 May 2022 / Online: 13 May 2022 (03:08:42 CEST)

How to cite: Orús-Lacort, M.; Jouis, C. Analyzing Collatz Conjecture Using the Mathematical Complete Induction Method. Preprints 2022, 2022050174 (doi: 10.20944/preprints202205.0174.v1). Orús-Lacort, M.; Jouis, C. Analyzing Collatz Conjecture Using the Mathematical Complete Induction Method. Preprints 2022, 2022050174 (doi: 10.20944/preprints202205.0174.v1).

Abstract

In this paper, we demonstrate the Collatz conjecture using the mathematical complete induction method. We show that this conjecture is satisfied for the first values of natural numbers, and in analyzing the sequence generated by odd numbers, we can deduce a formula for the general term of the Collatz sequence for any odd natural number n after several iterations. This formula is used in one case that we analyze using the mathematical complete induction method in the process of demonstrating the conjecture.

Keywords

number theory; Collatz conjecture

Subject

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

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