KöMaL 2008 B4113

Prove that if $a$ , $b$ , $c$ , $d$ are integers and $a$ + $b$ + $c$ + $d$ =0 then 2( $a^4$ + $b^4$ + $c^4$ + $d^4$ )+8 abcd is a square number.

Official text KöMaL. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.