GR-HMS 2017 Problem 3

Find all integer triples $(a,b,c)$ with $a>0>b>c$ whose sum equal $0$ such that the number $N=2017-a^3b-b^3c-c^3a$ is a perfect square of an 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.