I need help getting a proof, I don't want solution to the problem just help guiding me to complete the proof.
Suppose $m,n$ are coprime, Prove that $a \equiv b \mod{mn}$ if and only if:
$a \equiv b \mod{m}$, and
$a \equiv b \mod{n}$.
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Well it's if and only if claim so can you do either of the directions? – ploosu2 Mar 04 '14 at 20:52
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1What do you already know? Bezout's identity, Euclid's Lemma, any properties of lcm's? – Bill Dubuque Mar 04 '14 at 20:52
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I know only Bezout's identity and Euclid's Lemma – user133096 Mar 04 '14 at 20:54
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Then you can use this proof to infer $,(m,n)=1,,\ m,n\mid a-b,\Rightarrow, mn\mid a-b.\ \ $ – Bill Dubuque Mar 04 '14 at 21:15
