Question 2
For which integer pairs $(a,b)$ do there exist functions $f,g:\mathbb Z\to\mathbb Z$ such that $f(g(x))=x+a$ and $g(f(x))=x+b$ for every integer $x$?
Proposed by Ankan Bhattacharya. Evan Chen’s third-party compilation; source discussion https://aops.com/community/p12189493.
Proposed by Ankan Bhattacharya. Evan Chen’s third-party compilation; source discussion https://aops.com/community/p12189493.