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: 35


This is false, as $m^2-1 = (m+1)(m-1)$

Work Step by Step

Since $m^2-1 = (m-1)(m+1)$, for any $m \geq 3$, the expression must have at least 2 factors greater than 1, so it cannot be prime. Therefore, the statement is contradicted.
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