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Function with factorial

Source: Shortlist BMO 2018, N2; Albania TST problem 1; Macedonia TST problem 4

May 2, 2019
functionfactorialnumber theory

Problem Statement

Find all functions f:N→Nf:\mathbb{N}\rightarrow\mathbb{N} such that n!+f(m)!∣f(n)!+f(m!)n!+f(m)!|f(n)!+f(m!) for all m,n∈Nm,n\in\mathbb{N} Proposed by Valmir Krasniqi and Dorlir Ahmeti, Albania
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