In this paper, a formula to find the solutions of a congruence of prime power modulus of higher degree the type ??≡ ? (??? ??), where p is an odd positive prime integer and n≥ ?,is any positive integer, is established. The formula is of great merit and of time-saving in calculation.The method found in the Mathematicsliterature is time-consuming. It is also found that such a congruence is solvable if ??≡ ? (??? ??) and each congruence has exactly p solutions and in total, there are (p-1) such congruence.

Keywords : Binomial Expansion; Fermat’s Theorem Primepower modulus.