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Product divisible with factorial

Source: Kvant Magazine No. 9 2022 M2716

March 8, 2023
Kvantnumber theoryfactorial

Problem Statement

Find all pairs of natural numbers (k,m)(k, m) such that for any natural nn{} the product(n+m)(n+2m)⋯(n+km)(n+m)(n+2m)\cdots(n+km)is divisible by k!k!{}.
Proposed by P. Kozhevnikov
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