Theoretical Mathematics & Applications

A Brand new Approach to Collatz Conjecture

• [ Download ]
• Times downloaded: 8500

• 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.