CH-SMO 2010 Problem 3

For $n\in\mathbb{N}$ , determine the number of natural solutions $(a,b)$ such that $(4a-b)(4b-a)=2010^n$ holds.

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.