KöMaL 2020 A778

Find all square-free integers $d$ for which there exist positive integers $x$ , $y$ and $n$ satisfying $x^2+dy^2 = 2^n$ .

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.