(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The problem went "If c|a and c|b then c|gcd(a,b) where cεN and a,bεZ"

2. Relevant equations

3. The attempt at a solution

My proof went like this " Let a=cr and b=cs where r,sεZ. We want to show c|gcd(a,b). Lets

start with cd=ax+by where d,x,yεZ since the gcd(a,b) can be rewritten as a linear combination.

Substituting a and b we get cd=(cr)ax+(cs)ay <=> cd=c(rax+say) where rax+sayεZ. Hence

c|gcd(a,b).

is this right?

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# Homework Help: Proof using greatest common divisor.

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