KMO 2008 Problem 2

Find all integer polynomials $f$ such that there are infinitely many pairs of relatively prime natural numbers $(a,b)$ so that $a+b \mid f(a)+f(b)$ .

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.