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- Sat Dec 26, 2020 4:26 pm
- Forum: Asian Pacific Math Olympiad (APMO)
- Topic: APMO 2019 P1
- Replies: 1
- Views: 64621
Re: APMO 2019 P1
The only solution is $f(a)=a$ for all $a \in \mathbb{Z}^+$. It is easy to see that this solution works. We now prove that this is the only solution. Let $P(a,b)$ denote the assertion in the problem. First, we have \begin{align*}f(a)+b &|a^2+f(a)f(b)\\ \Longrightarrow f(a)+b &|a^2+f(a)f(b)-f(b)\left(...