1. The problem statement, all variables and given/known data For all natural numbers, a and b, if a and b are both even, then (a^2+b^2) is not a perfect square. (prove this) 2. Relevant equations 3. The attempt at a solution I tried proving by contradiction and got (2s)^2 +(2t)^2 =k^2. which translates to 4s^2 +4t^2=k^2. I don't know how to form the contradiction from here. Is it even possible?