Chinese Remainder Theorem Calculator

The Chinese Remainder Theorem is a theorem in number theory that provides a solution to a system of simultaneous congruences. In simpler terms, it helps find a unique solution to a set of equations with remainders. The theorem states that if we have a system of congruences, where each equation is of the form x ≡ a (mod m), and the moduli (m values) are pairwise coprime (meaning they have no common factors), then there exists a unique solution for x that satisfies all the congruences. The Chinese Remainder Theorem is valuable in various areas, including cryptography, number theory, and modular arithmetic. It allows for efficient computations involving large numbers and provides a method to reconstruct information from partial or encoded data.