CWMO 2004 Problem 1

Find all integers $n$ , such that the following number is a perfect square $N= n^4 + 6n^3 + 11n^2 +3n+31.$

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.