Number Theory


L' Attraction Des Nombres Par la Force Syracusienne

Authors: M. Sghiar

I show here that if $ x \in \mathbb{N}^*$ then $1 \in \mathcal{O}_S (x)= \{ S^n(x), n \in \mathbb{N}^* \} $ where $ \mathcal{O}_S (x)$ is the orbit of the function S defined on $\mathbb{R}^+$ by $S(x)= \frac{x}{2} + (x+\frac{1}{2}) sin^2(x\frac{\pi}{2})$, and I deduce the proof of the Syracuse conjecture.

Comments: 7 Pages. Accepted & french version © Copyright 2018 by M. Sghiar. All rights reserved. Respond to the author by email at:

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Submission history

[v1] 2018-12-08 16:12:41
[v2] 2018-12-13 06:58:30

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