Analyzing the Collatz Conjecture Using the Mathematical Complete Induction Method

被引：3

作者：

Orus-Lacort, Mercedes ^{[1
,2
]}

Jouis, Christophe ^{[3
,4
]}

机构：

[1] Univ Oberta Catalunya, Coll Math, Rambla Poblenou 156, Barcelona 08018, Spain

[2] Univ Nacl Educ Distancia, Coll Math, Calle Pintor Sorolla 21, Valencia 46002, Spain

[3] Univ Sorbonne Nouvelle Paris 3, Dept Langues Etrangeres Appl LEA, F-75005 Paris, France

[4] Ctr Anal & Math Sociales CAMS, F-75006 Paris, France

来源：

MATHEMATICS | 2022年 / 10卷 / 12期

关键词：

number theory; Collatz conjecture;

D O I：

10.3390/math10121972

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：7

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