My input is probably trivial but I thought it would be nice to prove it formally.
We need : gcd(x,y) = gcd(y,x)
Suppose gcd(x,y) = d. Then x = nd and y = md for some integers n,m where gcd(n,m) = 1.
So gcd(y,x) = gcd (md,nd) = d because gcd(m,n) =1.
We have shown for all x,y that gcd(x,y) =...