Functions and rational numbers
Source: 2019 Second Round - Poland
July 8, 2019
functionsrational numbersalgebranumber theoryfunction
Problem Statement
Let . Decide if there exist rational numbers and positive integers such that and:
\begin{align*}
\underbrace{f(f(\ldots f(f}_{m \ times}(x))\ldots)) = \underbrace{f(f(\ldots f(f}_{n \ times}(y))\ldots)).
\end{align*}