OMCC 2000 Problem 1

Find all three-digit numbers $abc$ (with $a \neq 0$ ) such that $a^{2}+b^{2}+c^{2}$ is a divisor of 26.

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.