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f(n(f(m)) <= nm

Source: 2021 IMOC qualification problem, A3

December 30, 2021
functionFunctional inequalityfunctionalinequalitiesalgebra

Problem Statement

Find all injective function f:N→Nf: N \to N satisfying that for all positive integers m,nm,n, we have: f(n(f(m))≤nmf(n(f(m)) \le nm
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