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 4.3 - Page 179: 40

Answer

(a) Yes (b) Yes

Work Step by Step

(a) Given $12a=25b$ or $3\cdot4\cdot a=5^2\cdot b$, we can see that there are no common factors among the numeric parts on both sides, thus we can conclude that $12|b$ and $25|a$. (b) Given $10x=9y$ or $2\cdot5\cdot x=3^2\cdot y$, we can see that there are no common factors among the numeric parts on both sides, thus we can conclude that $10|y$ and $9|x$.
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