APMO 2021 P5 - Determine all such functions

Discussion on Asian Pacific Mathematical Olympiad (APMO)
User avatar
Anindya Biswas
Posts: 255
Joined: Fri Oct 02, 2020 8:51 pm
Location: Magura, Bangladesh
Contact:

APMO 2021 P5 - Determine all such functions

Unread post by Anindya Biswas » Wed Jun 09, 2021 5:27 pm

Determine all functions $f:\mathbb{Z}\to\mathbb{Z}$ such that $f(f(a)-b)+bf(2a)$ is a perfect square for all integers $a$ and $b$.
"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
John von Neumann

Post Reply