Analyzing the Collatz Conjecture Using the Mathematical Complete Induction Method

Mercedes Orús-Lacort and Christophe Jouis
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Mercedes Orús-Lacort: College Mathematics, Universitat Oberta de Catalunya, Rambla del Poblenou 156, 08018 Barcelona, Spain
Christophe Jouis: Département Langues Etrangères Appliquées (LEA), Université de la Sorbonne Nouvelle Paris 3, 75005 Paris, France

Mathematics, 2022, vol. 10, issue 12, 1-7

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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