AT-OEMO-FED1 2002 Problem 1

Determine all integers $a$ and $b$ such that $(19a + b)^{18} + (a + b)^{18} + (a + 19b)^{18}$ is a perfect square.

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.