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Integer functions fulfilling a double inequality

Source: Balkan MO 2002, problem 4

April 24, 2006
functioninequalitiesalgebra proposedalgebra

Problem Statement

Determine all functions f:N→Nf: \mathbb N\to \mathbb N such that for every positive integer nn we have: 2n+2001≤f(f(n))+f(n)≤2n+2002. 2n+2001\leq f(f(n))+f(n)\leq 2n+2002.
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