If gcd(a,b)=c, prove C^2|ab

I have tried going c=ma+nb, but I am not sure where to go after here, squaring it seems to show me nothing, any advice to get me going on this?

Question

If  gcd(a,b)=c, prove C^2|ab

I have tried going c=ma+nb, but I am not sure where to go after here, squaring it seems to show me nothing, any advice to get me going on this?

dumbcow · Answer

try this:

a = mc
b = nc

ab = (mc)(nc) = mnc^2

thus c^2 divides evenly into mnc^2