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.
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For pairwise coprime positive integers , reduction induces a ring isomorphismEquivalently, every list of residue classes modulo the has a unique simultaneous residue class modulo their product.