Sum of $2$ equal squares also a square 
Is there an integer solution to $a^2 + a^2 = b^2$? Because there's this universift that has this logo of the pytagorean theorem where the two squares are equal, but I don't think it's possible.

We have $$2a^2=b^2,$$ which rearranges to $$2=\frac{b^2}{a^2}=\left(\frac{b}{a}\right)^2.$$
Hence there are integers $a,b$ solving this exactly if $\sqrt{2}$ is rational, which it isn't (see many proofs on wikipedia).  Thus there are no $a,b$ as desired.
