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 4.4 - Page 190: 43



Work Step by Step

The only possible residue mod $8$ for squares of odd integers is $1$, which corresponds to residues of $1$ and $9$ mod 16. Squaring each of these, we get $1$ mod $16$, so $n^4$ is $1$ mod $16$ if n is odd.
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