SILK-ROAD 2021 Problem 4

Integers $x,y,z,t$ satisfy $x^2+y^2=z^2+t^2$ and $xy=2zt$ prove that $xyzt=0$ Proposed by $M. Abduvaliev$

Dataset text AI-MO AoPS. 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.