Saturday, 5 September 2015

Elementary number theory proof involving multiplied gcd's

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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