Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 4 - Section 4.1 - Divisibility and Modular Arithmetic - Exercises: 13

Answer

a) 10 b) 8 c) 0 d) 9 e) 6 f) 2

Work Step by Step

Find the integer $c$ with 0≤$c$≤12 s.t. a) $c≡9(4$ mod 13) mod 13=36 mod 13 $c≡2(13)+10$ mod 13, so $c$ is within the desired domain is 10. b) $c≡11(9$ mod 13) mod 13=99 mod 13 $c≡7(13)+8$ mod 13, so $c$ is within the desired domain is 8. c) $c≡(4$ mod 13+9 mod 13) mod 13=(13 mod 13) mod 13=13 mod 13 $c≡0(13)+0$ mod 13, so $c$ within the desired domain is 0. d) $c≡(2(4$ mod 13)+3(9 mod 13)) mod 13=(8+27) mod 13=35 mod 13 $c≡2(13)+9$ mod 13, so $c$ is within the desired domain is 9. e) $c≡((4$ mod 13)$^2$+(9 mod 13)$^2$) mod 13 =(16 mod 13+81 mod 13) mod 13 =64 mod 13−729 mod 13=97 mod 13 $c≡7(13)+6$ mod 13, so c is within the desired domain is 6. f) $c≡((4$ mod 13)$^3$−(9 mod 13$^3$)) mod 13=64 mod 13−729 mod 13 =665 mod 13 $c≡$51(13)+2 mod 13, so c is within the desired domain is 2.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.