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: 31

Answer

a) 6 mod 369 b) 64 mod 2859 c) 441 mod 2116 d) 216 mod 74250

Work Step by Step

a) (19$^2$ mod 41) mod 9 (361 mod 41) mod 9 (33 mod 41) mod 9 6 mod 369 b) (32$^3$ mod 13)$^2$ mod 11 (32768 mod 13)$^2$ mod 11 (8 mod 13)$^2$ mod 11 64 mod 2859 c) (7$^3$ mod 23)$^2$ mod 31 (49*7 mod 23)$^2$ mod 31 (21 mod 23)$^2$ mod 31 (441 mod 529) mod 31 441 mod 2116 d) (21$^2$ mod 15)$^3$ mod 22 (441 mod 15)$^3$ mod 22=(6 mod 15)$^3$ mod 22 =(216 mod 3375) mod 22=216 mod 74250
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