A Simple Proof on Fermat’s Last Theorem in Case of n=3

Abstract

Fermat’s last theorem was proposed more than 350 years ago, it attracted the interests of a lot of researchers [1-11]. The simplest case of Fermat’s last theorem is n=3, but the previous proofs on it are generally complex or not easy to understand. The present work through the transformation x=t+1, firstly proves that when the values of x and t { tmin, tmax} { xmin, xmax }, the Fermat’s last theorem in the case of n=3 is true. Furthermore, the paper also proves that when x take other positive integers besides x { tmin, tmax} {xmin, xmax}, the Fermat’s last theorem in the case of n=3 is true as well. Therefore, there are no a group of positive integers of x, y and z to satisfy the Diophantine equation in the case of n=3; Fermat’s last theorem in the case of n=3 is true.