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 163: 58


This is true.

Work Step by Step

Let the integers be $b$ and $b+1$. Expanding, we find that their squares are (respectively) $b^2$ and $b^2+2b+1$. Subtracting, we get $2b+1$, which is (by definition) odd, so the statement is true.
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