SE-SKOLORNAS 1998 Problem 1

Find all positive integers $a, b, c$ , such that $(8a-5b)^2 + (3b-2c)^2 + (3c-7a)^2 = 2$ .

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.