Chinese Remainder Theorem

The CRT states roughly that any positive integer \(m\) is uniquely defined by its remainder modulo \(k\) co-prime integers \(p_1\), \(p_2\), \(\ldots\), \(p_k\) if \(m < \prod\limits_{i=1}^k p_i\).

Co-prime means all \(k\cdot (k-1)\) combinations are prime with respect to each other.