HMMT 2005 U1

Find the largest positive integer $n$ such that $1+2+3+\cdots+n^{2}$ is divisible by $1+2+$ $3+\cdots+n$ .

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.