FERMAT’S LAST THEOREM IS EQUIVALENT TOBEAL’S CONJECTURE

Abstract

It is proved in this paper that (1) Fermat’s Last Theorem: If π is an odd prime, there are no relatively prime positive integers x,y,z satisfying the equation z^π = x^π+y^π, and (2) Beal’s Conjecture :The equation z^ξ = x^µ +y^ν has no solution in relatively prime positive integers x,y,z with µ,ξ and ν odd primes at least 3. It is also proved that these two statements, (1) and (2), are equivalent.