DE-MO 1999 Problem 1

Find all $x,y$ which satisfy the equality $x^2 +xy+y^2 = 97$ , when $x,y$ are a) natural numbers, b) integers

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.