A COMPUTATIONAL EXPLORATION OF THE CHINESE REMAINDER THEOREM

Real life problems can be expressed as a congruence modulus n and split into a system of congruence equations in modulus factors of n. A system of congruence equations can be combined into a congruence equation under certain conditions. This paper uniquely presents and critically reviews the generalized Chinese Remainder Theorem (CRT) for combining systems of congruence equations into single congruence equations. Sequential and parallel implementation strategies of the generic CRT are outlined. A variety of unique applications of the CRT are discussed.