Fermat's Last Theorem for Special Case

Abstract

In this paper we present an elementary proof for a special case of Fermat's last theorem for specific category of a, b and c. In fact, we assume that $n$ is prime and $4\rvert (n+1),$ then for $a,b$ and $c$ that $ n\nmid abc$ the equation $a^{2n} = b^{2n} + c^{2n}$ does not have any solution in natural numbers.