I have tried to get $4$ integers $a, b,c, d \neq 0$ such that both of $a+b$, $c+d$ and $a+d, b+c$ are perfect square yield to $a+b+c+d$ is a perfect square ? , I have tried to solve the following system but I can't solve $(x+y+z+r=p^2, x+y=a^2, z+r=b^2,a^2+b^2=c^2)$ it in integers ?Any help ?
2026-03-29 16:39:53.1774802393
Are there non null four integers such that sum of each two is a perfect square and sum all of them also perfect square?
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