Theoretical Mathematics & Applications

A Brand new Approach to Collatz Conjecture

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  • Abstract

     

    The aim of this paper is to propose a brand new approach on Collatz conjecture as well as a proof of it. The method is based on the fundamental theorem of arithmetics and on a definition of trajectories that implies a contradiction to the latter theorem when a divergence or looping of the algorithm is assumed. This contradiction proves Collatz conjecture.

     

    Mathematics Subject Classification: 11A51, 11Y05, 11Y11.

    Keywords: Conjecture, Collatz, Syracuse, 3n+1, Trajectory.