The sequence $ (F_n)$ of Fibonacci numbers satisfies $ F_1 = 1, F_2 = 1$ and $ F_n = F_{n-1} +F_{n-2}$ for all $ n \ge 3$. Find all pairs of positive integers $ (m, n)$, such that $ F_m . F_n = mn$.
Source: Final Round Grade 11 Pro 3
Tags: induction, number theory unsolved, number theory
The sequence $ (F_n)$ of Fibonacci numbers satisfies $ F_1 = 1, F_2 = 1$ and $ F_n = F_{n-1} +F_{n-2}$ for all $ n \ge 3$. Find all pairs of positive integers $ (m, n)$, such that $ F_m . F_n = mn$.