Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 4 - Elementary Number Theory and Methods of Proof - Exercise Set 4.1 - Page 161: 4

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.
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