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Product divisible by factorial

Source: BdMO 2024 Secondary National P9

March 18, 2024
number theoryfactorialDivisibilityp-adic

Problem Statement

Find all pairs of positive integers (k,m)(k, m) such that for any positive integer nn, the product(n+m)(n+2m)⋯(n+km)(n+m)(n+2m)\cdots(n+km)is divisible by k!k!.
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