CONO-SUR 1998 Problem 4

Find all functions $R-->R$ such that: $f(x^2) - f(y^2) + 2x + 1 = f(x + y)f(x - y)$

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.