IrMO 2006 Problem 1

Are there integers $x,y$ and $z$ which satisfy the equation $z^2=(x+1)(y^2-1)+n$ when (a) $n=2006$ (b) $n=2007$ ?

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.