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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)
A peer-reviewed article of this Preprint also exists.
Orús-Lacort, M.; Jouis, C. Analyzing the Collatz Conjecture Using the Mathematical Complete Induction Method. Mathematics 2022, 10, 1972. Orús-Lacort, M.; Jouis, C. Analyzing the Collatz Conjecture Using the Mathematical Complete Induction Method. Mathematics 2022, 10, 1972.
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
Computer Science and Mathematics, Applied Mathematics
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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