An Alternative Elementary Proof for Fermat's Last Theorem

Abstract: Fermat’s Last Theorem states that the equation x n + y n = z n has no solution for x, y and z as positive integers, where n is any positive integer > 2. Taking the proofs of Fermat and Euler for the exponents n = 4 and n = 3, it would suffice to prove the theorem for the exponent n = p, where p is any prime > 3. We hypothesize that r, s and t are positive integers satisfying the equation r p + s p = t p and establish a contradiction in this proof. We include another Auxiliary equation x 3 + y 3 = z 3 and connect these two equations by using transformation equations. On solving the transformation equation we get rst = 0, thus proving that only a trivial solution exists in the main equation r p + s p = t p .