FI-MO 2016 Problem 1

Which triangles satisfy the equation $\frac{c^2-a^2}{b}+\frac{b^2-c^2}{a}=b-a$ when $a, b$ and $c$ are sides of a triangle?

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.