Proof of Fermat Last Theorem Based on Odd Even Classification of Integers

Abstract

In the middle of 17th century, Pierre de Fermat mentioned that no value of n > 2 could satisfy the equation x n + y n = z n , where n, x, y and z are all positive integers. The statement is popularly known as Fermat’s last theorem. An acceptable mathematical proof of this theorem is being explored still today. When searched online treasures of resources, one may find various proofs of this theorem. In this paper I am not discussing any historical attempts that failed or partially succeeded. I am going to discuss the approach which I have adopted to proof this theorem. The approach is based on odd-even classification of positive integers. Assumption that the equation x n + y n = z n , where n, x, y and z are all positive integers, has a solution for n > 2 leads to some contradiction.