FI-MO 2016 Problem 4

How many pairs $(a, b)$ of positive integers $a,b$ solutions of the equation $(4a-b)(4b-a )=1770^n$ exist , if $n$ is a positive integer?

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.