An Alternative Elementary Proof for Fermat's Last Theorem
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Abstract
Fermat’s Last Theorem states that the equation xn + y n = zn 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 + sp = tp and establish a contradiction in this proof. We include another Auxiliary equation x 3 + y3 = z3 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 + sp = tp .
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