Number Theory

    

Proof of the Collatz Conjecture

Authors: Fabrice Trifaro

The Collatz conjecture, also known as the Syracuse conjecture or the 3x+1 problem, is a mathematical conjecture according to which the Collatz sequence always reaches the value 1, and then repeats the cycle (1,4,2) indefinitely, regardless of the first term of the sequence as long as it is a strictly positive integer. It originated in the 1930s and its authors are mainly Lothar Collatz and Helmut Hasse, the latter shared it in the United States during a visit to Syracuse University, and the Collatz sequence then became known as the Syracuse sequence. To date, this conjecture has not been proven either true or false. The purpose of this study is to prove, as clearly and precisely as possible, that this conjecture is true. The proof is based on classical mathematics which should not pose any major difficulties.

Comments: 16 Pages.

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[v1] 2025-02-14 11:24:45

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