Fermat’s Last theorem Algebraic Proof

Abstract

In 1995, A, Wiles announced, using cyclic groups ( a subject area which was not available at the time of Fermat), a proof of Fermat’s Last Theorem, which is stated as follows: If π is an odd prime and x, y, z, are relatively prime positive integers, then z π 6= x π + y π . In this note, an elegant proof of this result is given. It is proved, using elementary algebra, that if π is an odd prime and x, y, z are positive integers satisfying z π = x π +y π , then z, x, are each divisible by π.