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The aim is to establish a mathematical proof of the Collatz conjecture, a famous unsolved problem in mathematics.

July 10, 2026Open Access

A Complete Proof of the Collatz Conjecture

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The aim is to establish a mathematical proof of the Collatz conjecture, a famous unsolved problem in mathematics.
Applied strong induction to show the conjecture holds for all natural numbers.
Utilized binary analysis to explore the properties of integer sequences involved.
Successfully proved that every positive integer eventually reaches 1 under the rules of the Collatz sequence.

Proven the Collatz conjecture using strong induction and binary analysis, indicating its validity.

In this paper, we prove the Collatz conjecture (3n+1 problem) using strong induction and binary analysis. Contact: +98 935 628 6975 (Iran)

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Abolfazl Shahraki (2026) studied this question.

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Proven the Collatz conjecture using strong induction and binary analysis, indicating its validity.

In this paper, we prove the Collatz conjecture (3n+1 problem) using strong induction and binary analysis. Contact: +98 935 628 6975 (Iran)