TUYMAADA 2018 S5

A prime $p$ and a positive integer $n$ are given. The product $(1^3+1)(2^3+1)...((n-1)^3+1)(n^3+1)$ is divisible by $p^3$ . Prove that $p \leq n+1$ .

Proposed by Z. Luria

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.