Simplified Proof of the Collatz Conjecture Using Regularity General solution‐Calculation Method by Multiples of 6 and Remainder

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Abstract

In solving the Collatz conjecture, it turns out that if we let all integers k be 6n, 6n+1, 6n+2, 6n+3, 6n+4, 6n+5, then we can solve the Collatz conjecture periodically. The Collatz conjecture states that for any positive integer P (initial value), if n is even, divide n by 2; if n is odd, repeat the rule of multiplying n by 3 and adding 1, which always converges to 1. One open problem has been proved by this paper. The authors hope to contribute to the mathematical community by presenting simple proofs of conjectures in the history of mathematics such as the Collatz conjecture.

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europepmc
last seen: 2026-05-20T01:45:00.602351+00:00
unpaywall
last seen: 2026-05-27T02:00:06.600101+00:00
License: CC-BY-4.0