KöMaL 2025 B5481

Prove the following divisibility for every positive integer $n$ : $(n!)^n \mid n^2 \cdot (n^2-1) \cdot (n^2-2) \cdot \ldots \cdot (n+2) \cdot (n+1).$

Official text KöMaL. Quoted with source.

Solutions

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