English

Abstract

Fermat's Last Theorem stated, without proof, that the equation, X n + Y n = Z n , where X, Y, Z and n are integers greater than 2, had no solution for X, Y and Z co-primes. This Theorem was proven by Andrew Wiles in 1994 using mathematical techniques unknown to Fermat 350 years ago. Andrew Beal posed a related conjecture that the equation X a + Y b = Z c had no solution for X, Y, Z, a, b, and c, where they are all integers greater than 2, and X, Y and Z are co-primes. A simple mathematical proof available to Fermat is used here to prove the Beal conjecture. Then multiplying each term by finite X n-2 we obtain, X n + X n-2 Y 2 = X n-2 Z 2 (3) and we can then write it as X n + Y n (X n-2 /Y n-2 ) = Z n (X n-2 / Z n-2 ) (4). We now compare this to Fermat's target relationship for n > 2, X n + Y n = Z n (5). From (4) and (5) if both are true we