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Possible Duplicate:
Prove the Chinese Remainder Theorem

Suppose $gcd(m, n) = 1$. Show that for every pair of integers $a, b$, there exists an integer $x$ such that

$x \equiv a \pmod m$ and $x \equiv b \pmod n$

By $gcd$ I mean greatest common divisor.

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    See [Chinese remainder theorem](http://en.wikipedia.org/wiki/Chinese_remainder_theorem).2012-01-30

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