Article
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Goldbach Conjecture and the Trichotomy Law
Version 1
: Received: 5 October 2022 / Approved: 7 October 2022 / Online: 7 October 2022 (08:34:21 CEST)
How to cite: Sharma, A.U. Goldbach Conjecture and the Trichotomy Law. Preprints 2022, 2022100077. https://doi.org/10.20944/preprints202210.0077.v1 Sharma, A.U. Goldbach Conjecture and the Trichotomy Law. Preprints 2022, 2022100077. https://doi.org/10.20944/preprints202210.0077.v1
Abstract
This paper asserts that the falsity of Goldbach Conjecture results in the breakdown of Trichotomy Law. Assuming that Goldbach Conjecture breaks down at an even integer 2n, where n ≥ 3, we note that the differences of 2n with the odd primes in the interval (1, n) are composite integers. We form a product δ of the collection of the least prime factors of these composite integers. We show that for a base case this product breaks Trichotomy Law. With the inductive hypothesis that such is the case with 2n, we prove that for all even integers the breakdown of Goldbach Conjecture entails the breakdown of Trichotomy Law.
Keywords
Goldbach Conjecture; Trichotomy Law
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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