MathDB

Let

\mathbb{Z}

be the set of all integers. Find all pairs of integers

(a,b)

for which there exist functions

f \colon \mathbb{Z}\rightarrow \mathbb{Z}

and

g \colon \mathbb{Z} \rightarrow \mathbb{Z}

satisfying f(g(x))=x+a \text{and} g(f(x))=x+b for all integers

x

.
Proposed by Ankan Bhattacharya

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