Abstract
Abstract: 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 Mathematics literature is timeconsuming.
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, Prime-power modulus
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