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 162: 49

Answer

This statement is true.

Work Step by Step

Let the first integer be $2k+1$ and let the second integer be $2m+1$ with $k>m$ --this is necessary for two odd integers. Then, subtracting, we get $(2k+1)-(2m+1) = 2k-2m = 2(k-m)$, which must be even, as 2 divides it. Therefore, the statement is proven
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