Fucheng Zhu

A Proof of the Collatz Conjecture via Modulo‑4 Congruence Classification

The Collatz conjecture, also known as the Hailstone conjecture, states that for any positive integer n, define the iterative transformation rule: divide an even number by 2 directly; if n is odd, calculate 3n+1. All positive integers will converge to 1 after finite iterations.Thi...