On the Collatz Conjecture

Yao Moïse Blewoussi

Journal of Mathematics Research, 2024, vol. 14, issue 6, 28

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.

Date: 2024
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