PL-OM 1996 Problem 1

Find all pairs $(n,r)$ with $n$ a positive integer and $r$ a real such that $2x^2+2x+1$ divides $(x+1)^n - r$ .

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.