I'm having trouble proving the following if and only if statement:
For all integers a,b,n, prove that n|gcd(a,n)gcd(b,n) if and only if n|ab
For proving n|gcd(a,n)gcd(b,n)⟹n|ab, I tried using Bezout's Lemma for both gcds and expanding but didn't know how to show that n divided ab.
Also didn't didn't how to approach the converse. Any help?
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