About Fermat’s Last Theorem

In this paper, the possibility of finding a simple proof of Fermat’s Last Theorem is discussed by using the principles of elementary algebra instead of using the Modularity theorem. For an odd prime n the Fermat’s diophantine equation xn = yn + zn gives rise to an equation of (n − 1)th degree which can be proved to be irreducible over the field Q of rational real numbers by using Eisenstein’s criterion. This proves the theorem for any odd prime n. For n = 4 we use a method of reductio-ad-absurdum to prove the theorem. Finally, we deduce Beal’s conjecture.