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.