Question 1
Find all functions $f:\mathbb N\to\mathbb N$ satisfying $f(a^2+b^2)=f(a)f(b)$ and $f(a^2)=f(a)^2$ for all positive integers $a,b$. Here $\mathbb N$ denotes the positive integers.
Proposed by Vincent Huang. Evan Chen’s third-party compilation; source discussion https://aops.com/community/p21498724. Source video https://youtu.be/9WNgDETHOlI?t=63.
Proposed by Vincent Huang. Evan Chen’s third-party compilation; source discussion https://aops.com/community/p21498724. Source video https://youtu.be/9WNgDETHOlI?t=63.