OMCPLP 2016 Problem 6

Source: Lusophon MO 2016 Prove that any positive power of $2$ can be written as: $5xy-x^2-2y^2$ where $x$ and $y$ are odd numbers.

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.