Prove: for all positive integers $m, n$ $\frac 1m + \frac 1{m+1} + \dotsb + \frac 1 {m+n} $ is not an integer.
Source: 2021 IMOC qualification problems, N2
Tags: IMOC, number theory
Prove: for all positive integers $m, n$ $\frac 1m + \frac 1{m+1} + \dotsb + \frac 1 {m+n} $ is not an integer.