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 4.3 - Primes and Greatest Common Divisors - Exercises - Page 272: 17

Answer

a) yes b) no c) yes d) yes

Work Step by Step

a) The numbers 11, 15=3*5, and 19 are pairwise relatively prime because there are no factors shared between two of them. b) The numbers 14=2*7, 15=3*5, and 21=3*7 are not pairwise relatively prime because both 15 and 21 have a factor of 3. c) The numbers $12=2^2*3$, 17, 31, and 37 are pairwise relatively prime because no two of them share a factor. d) The numbers $7, 8=2^3, 9=3^2,$ and 11 are pairwise relatively prime because none of them share a factor with any of the others.
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