Chinese remainder theorem

The Chinese Remainder Theorem (CRT) is a result in number theory that provides a way to solve systems of simultaneous congruences with different moduli. It states that if you have several congruences with pairwise coprime moduli, there exists a unique solution modulo the product of those moduli. ### Formulation If \( n_1, n_2, \ldots, n_k \) are pairwise coprime integers (i.e.