Let f(t)=t3+t. Decide if there exist rational numbers x,y and positive integers m,n such that xy=3 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*} functionsrational numbersalgebranumber theoryfunction