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Published December 26, 2025 | Version v8
Journal article Open

Proof of the Collatz Conjecture

Description

The Collatz Conjecture (or 3n+1 problem) has been explored for about 86
years. In this article, we prove the Collatz Conjecture. We will show that
this conjecture holds for all positive integers by applying the Collatz inverse
operation to the numbers that satisfy the rules of the Collatz Conjecture.
Finally, we will prove that there are no positive integers that do not satisfy
this conjecture.

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