Numerical Approach for Fermat's last theorem

Abstract: This research focuses on the Numerical approach for Fermat's Last theorem. We can induce an Alternative form of Fermat's last theorem by using particular geometric mapping $\mathcal{M}$ on a Cartesian plane to a Torus. It transforms the Fermat's Last Theorem to finding a rational cross point between two parametric curves on the torus. In the end, this research shows the movement of the point, on the line $x^n+y^n=1$, has an acceleration phase transition near ($x,n$)=(0,2). Moreover, the studies about the relationship between this acceleration transition and the solution for the Fermat's Diophantine equation in the case of $n>$2, need further investigation.