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Proofing the Collatz Conjecture by Mathematical Induction
Zhang Tianshu
Zhanjiang city, Guangdong province, China
Email: chinazhangtianshu@126.com
china.zhangtianshu@
Abstract
In this article, the author applies the mathematical induction, classifies
positive integers, and passes operations according to the operational rule,
to achieve the goal that proves the Collatz conjecture finally.
AMS subject classification: 11P81, 11A25 and 11Y55
Keywords: Collatz conjecture, mathematical induction, operational
routes, classify positive integers, the operational rule
1. Introduction
The Collatz conjecture is also variously well-known 3n+1 conjecture, the
Ulam conjecture, Kakutani’s problem, the Thwaites conjecture, Hasse’s
algorithm, and the Syracuse problem etc. Yet it is still both unproved and
un-negated a conjecture ever since named after Lothar Collatz in 1937.
2. Basic Concepts and Criteria
The Collatz conjecture states that take any positive integer n, if n is an
even number, then divide n by 2; if n is an odd number, then multiply n
by 3 and add 1. Repeat the above process indefinitely, then no matter
which positive integer you start with, it will eventually reach a result of 1.
Let us regard above-mentioned operational stipulations as the operational
rule of the conjecture or the operational rule for short.
1
Start with any positive integer to operate successive emerging positive
integers by the operational rule, afterwards, regard consecutive integers
plus synclastic arrowheads among them as an operational route.
If an integer (or an integer ’s expression) Pie exists at an operational route,
then may term the operational
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