In Search of an Elementary Proof for Fermat’s Last Theorem (Indian Journal of Advanced Mathematics (IJAM), 2026)
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 hypothesise that r, s, and t are positive integers satisfying the equation rp + sp = tp, and we establish a contradiction in this proof. We include another Auxiliary equation, x³ + y³ = z³, and connect these two equations by using the transformation equations. By solving the transformation equation, we prove that rst = 0, thus demonstrating that only a trivial solution exists in the central equation, r p + s p = t p .