A Possible Proof of Collatz Conjecture

Pen, Paper and PHP

Our reader Eswar Chellappa has sent his work on the solution of ‘3X+1′ problem, also called Collatz Conjecture. He had been working on the proof of Collatz Conjecture off and on for almost ten years. The Collatz Conjecture can be quoted as follow: Let $\phi : \mathbb{N} \to \mathbb{N}^+$ be a function defined  such that: $$\phi(x):= \begin{cases} \frac{x}{2}, & \text{if }…

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