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Another vp NT with factorials

Source: Polish MO Second round 2024 P6

February 10, 2024
factorialnumber theory

Problem Statement

Given is a prime number pp. Prove that the number p⋅(p2⋅pp−1−1p−1)!p \cdot (p^2 \cdot \frac{p^{p-1}-1}{p-1})! is divisible by ∏i=1p(pi)!.\prod_{i=1}^{p}(p^i)!.
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