MathDB
Functional Equations

Source: 2019 USAJMO 2, by Ankan

April 17, 2019
AMCUSA(J)MOUSAJMOfunctionalgebrafunctional equationHi

Problem Statement

Let Z\mathbb{Z} be the set of all integers. Find all pairs of integers (a,b)(a,b) for which there exist functions f ⁣:Z→Zf \colon \mathbb{Z}\rightarrow \mathbb{Z} and g ⁣:Z→Zg \colon \mathbb{Z} \rightarrow \mathbb{Z} satisfying f(g(x))=x+a  \text{and}  g(f(x))=x+b for all integers xx.
Proposed by Ankan Bhattacharya
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