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mn+1|f(m)f(n)+1

Source: 2022 Thailand Online MO P3

April 4, 2022
functionfunctional equationnumber theory

Problem Statement

Let N\mathbb{N} be the set of positive integers. Across all function f:N→Nf:\mathbb{N}\to\mathbb{N} such that mn+1 divides f(m)f(n)+1mn+1\text{ divides } f(m)f(n)+1 for all positive integers mm and nn, determine all possible values of f(101).f(101).
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