Method of Infinite Descent and proof of Fermat's last theorem for n=3

摘要

Fermat proved one of his theorems that the area of a Pythagorean triangle can not be a square of an integer using his powerful mathematical tool of method of infinite descent and the most general parametric solution of the corresponding equation. This proof can directly be used to prove his last theorem for although Euler proved it later using the method of infinite descent. It is well known that Euler’s proof of Fermat’s last theorem for (FLT3) using Fermat’s mathematical tool and a parametric solution of the equation is incomplete. It is pointed out that if Euler used the general parametric solution of the equation and the then available and rather old method of finding the roots of a cubic of Tartagalia and Cardan, proof of FLT3 could have done easily without making no room for an error.