Answer
Let $m=n=2$. Then $\frac{1}{m}+\frac{1}{n}=\frac{1}{2}+\frac{1}{2}=1$. Since $1$ is an integer, we conclude that there are integers $m$ and $n$ such that $\frac{1}{m}+\frac{1}{n}$ is an integer.
Work Step by Step
This proof is called a constructive proof of existence, whereby one shows that something exists by finding a specific example. For more on this, see the section "Proving Existential Statements" that begins on page 148, especially example 4.1.3.
