Solutions of a Class of Congruence of Multiple of Prime-Power Modulus of Higher Degree

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 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.