Theoretical Mathematics & Applications

Proof of the Collatz Conjecture

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  • Abstract 


    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. 


    Mathematics Subject Classification (2020): 11A25, 11A51, 11B50, 11B99. 
    Keywords: Collatz operation, Collatz inverse operation, Collatz numbers, Set theory.