Abstract

The Collatz conjecture (or Syracuse conjecture) states: all Syracuse sequences converge to 1. We present a Syracuse sequence, and we prove that the conjecture is true, first by using the fact that all convergent integer sequences are eventually constant. We then prove wrong 2 hypotheses: the case where the sequence tends to infinity, and the case where the sequence has no limit and is eventually periodic. We conclude by elimination, afterward.

This work is licensed under a Creative Commons Attribution 4.0 License.