MEMO 2021 Problem 7

Find all pairs $(n, p)$ of positive integers such that $p$ is prime and $1 + 2 + \cdots + n = 3 \cdot (1^2 + 2^2 + \cdot + p^2).$

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.