Proof of the first case of Format's Last Theorem is given. For definitions of terms used in the text, Fermat's Last Theorem which is referred can be stated as if p is an odd prime then xP yP zP = 0 has no solution in rational integers x, y and z which are pairwise coprime and such that x. y. z. t 0. if in given equation x, y and z are also prime to p which is called first case of Fermat's Last Theorem. Let R be the ring of integers in an algebraic number field K. If g is a primitive hh root of unity, let the cyclotomic field defined by g be denoted by K(E.).