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Functional Inequality with Divisibility Condition

Source: 2021 Macedonian Team Selection Test P5

May 30, 2021
Divisibilityfunctionsalgebra

Problem Statement

Determine all functions f:N→Nf:\mathbb{N}\to \mathbb{N} such that for all a,b∈Na, b \in \mathbb{N} the following conditions hold:
(i)(i) f(f(a)+b)∣ba−1f(f(a)+b) \mid b^a-1; (ii)(ii) f(f(a))≥f(a)−1f(f(a))\geq f(a)-1.
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