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Rational NT FE

Source: 2024 IMOC N6 (Night 4)

August 8, 2024
number theoryfunctional equation

Problem Statement

Find all functions f:Q+→Q+f:\mathbb{Q}^+\to\mathbb{Q}^+ such that xy(f(x)−f(y))∣x−f(f(y))xy(f(x)-f(y))|x-f(f(y)) holds for all positive rationals xx, yy (we define that a∣ba|b if and only if exist n∈Zn \in \mathbb{Z} such that b=anb=an) Proposed by supercarry & windleaf1A
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