Fermat’s Last Theorem Proved by Induction

EasyChair Preprint 3357

Abstract

A proof of Fermat’s last theorem is demonstrated. It is very brief, simple, elementary, and absolutely arithmetical. The necessary premises for the proof are only: the property of identity of the relation of equality, modus tollens, axiom of induction, the proof of Fermat’s last theorem in the case of “n = 3” as well as the premises necessary for the formulation of the theorem itself. It involves a modification of Fermat’s approach of infinite descent. The infinite descent is linked to induction starting from “n = 3” by modus tollens. An inductive series of modus tollens is constructed. The proof of the series by induction is equivalent to Fermat’s last theorem. As far as Fermat had been proved the theorem for “n = 4”, one can suggest that the proof at least for “n ≥ 4” had been accessible to him.

Keyphrases: Fermat's last theorem, identity, induction, infinite descent

@booklet{EasyChair:3357,
  author    = {Vasil Penchev},
  title     = {Fermat’s Last Theorem Proved by Induction},
  howpublished = {EasyChair Preprint 3357},
  year      = {EasyChair, 2020}}