Can p be an odd prime that divides both r^2-s^2 and r^2+s^2?

[awesome220]

Can anyone help me with this?

If gcd(r,s)=1 then prove that gcd(r^2-s^2, r^2+s^2)=1 or 2.

i'm so confused.

 

[morphism]

Let p be an odd prime that divides both r^2-s^2 and r^2+s^2. Show that this leads to a contradiction.