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n^3 - n^2 <= f(n) (f(f(n)))^2 <= n^3 + n^2

Source: 2019 Saudi Arabia IMO TST I p 1

July 28, 2020
algebraFunctional inequalityfunctional

Problem Statement

Find all functions f:Z+→Z+f : Z^+ \to Z^+ such that n3−n2≤f(n)⋅(f(f(n)))2≤n3+n2n^3 - n^2 \le f(n) \cdot (f(f(n)))^2 \le n^3 + n^2 for every nn in positive integers
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