This theorem provides a way to solve a system of congruences of the form x congruent to a_i modulo m_i, where m_i are pairwise relatively prime. If we let M equal the product of all m_i, then we can solve each congruence modulo m_i and then combine the solutions using the Chinese Remainder Theorem. If a solution exists, then it is unique modulo M and is the modular inverse of a modulo M.