(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Prove the sum of two even perfect squares is not a perfect square

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