I am stuck on this one too........let m,n be integers such that gcd(m,n)=1. prove that if a equivalent to b mod m and a equivalent to b mod n, then a equivalent to b mod (mn)

thanks

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- Apr 15th 2010, 07:59 PM #1

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- Apr 15th 2010, 08:19 PM #2
Since $\displaystyle a \equiv b \mod m$, we have $\displaystyle m \mid (a-b)$. Similarily $\displaystyle n \mid (a-b)$. Now you probably know that if $\displaystyle s \mid u$, $\displaystyle t \mid u$ and $\displaystyle (s,t)=1$ then $\displaystyle st \mid u$. What do you conclude?

- Apr 15th 2010, 08:26 PM #3

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- Apr 15th 2010, 09:02 PM #4

- Apr 15th 2010, 09:08 PM #5

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- Apr 16th 2010, 08:27 AM #6