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Function can't not satisfy this!

Source: 2024 Nepal TST P2

April 12, 2024
functionNatural Numbersinequalities

Problem Statement

Let f:N→Nf: \mathbb{N} \to \mathbb{N} be an arbitrary function. Prove that there exist two positive integers xx and yy which satisfy f(x+y)≤f(2x+f(y))f(x+y) \le f(2x+f(y)).
(Proposed by David Anghel, Romania)
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