- #1
bonfire09
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Homework Statement
The problem went "If c|a and c|b then c|gcd(a,b) where cεN and a,bεZ"
Homework Equations
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?