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The congruence relations EQN:n\equiv~a_1\pmod{m_1},\ldots,n\equiv~a_k\pmod{m_k} always have a unique solution for EQN:n\pmod{m_1\cdots~m_k} provided no two of the moduli have a common factor.

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* http://en.wikipedia.org/wiki/Chinese_remainder_theorem

* http://mathworld.wolfram.com/ChineseRemainderTheorem.html