A Proof for Fermat’s Last Theorem

Fermat’s proposition during 1637 that the Diophantine equation xn + yn = zn where x, y, z and n are integers has no solution for n > 2 has come to be known as Fermat’s Last Theorem. Taking the proofs of the theorem by Fermat and Euler for the index n = 4 and n = 3, it would suffice to prove the theorem for the index p which is any prime >3. We consider the equation rp + sp = tp to prove the theorem. We take another auxiliary equation x3 + y3 = z3 to substantiate the proof. Both equations have been combined by means of equivalent equations, into which we have employed the Ramanujan-Nagell equation. Solving the equivalent equations using the Ramanujan-Nagell Equation we prove the theorem.