Problem

Source: 2018 Taiwan TST Round 1

Tags: number theory



Find all pairs of integers $ \left(m,n\right) $ such that $ \left(m,n+1\right) = 1 $ and $$ \sum\limits_{k=1}^{n}{\frac{m^{k+1}}{k+1}\binom{n}{k}} \in \mathbb{N} $$