Arithmétique cantus, graphe de Syracuse, et preuve de la conjecture de Collatz

Nonvikan Karl-Augustt Alahassa (1)

1 Département de Mathématiques et de Statistiques [UdeM- Montréal]

The conjecture of Syracuse or Collatz's conjecture is an old conjecture relating to natural numbers. It was discovered by the German mathematician Lothar Collatz in 1930. Since then, many mathematicians have sought to explain why this conjecture is true, but today no one has yet arrived. We have provided a complete proof of this, thanks to a new arithmetic called cantus arithmetic. This arithmetic allowed us to prove the connexity of the Syracuse graph. By reconstructing the graph from a process of generative deterministic branching, we have shown that we always reach to 1, with any number taken at the start.

Domaines: Théorie des nombres [math.NT]; Mathématiques générales [math.GM]; Logique [math.LO]

Nonvikan Karl-Augustt Alahassa. Arithmétique cantus, graphe de Syracuse, et preuve de la conjecture de Collatz. 2017. ⟨hal-01522391v2⟩