CIIM 2020 Problem 2

Find all triples of positive integers $(a,b,c)$ such that the following equations are both true: I- $a^2+b^2=c^2$ II- $a^3+b^3+1=(c-1)^3$

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.