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 189: 22

Answer

$0$

Work Step by Step

If $c\ mod\ 15=3$, then $c=15q+3$ for some integer $q$. Multiplying both sides by $10$, we get $10c=10(15q+3)$$=15(10q)+30$$=15(10q)+15(2)=15(10q+2)+0$. Since $10q+2$ is an integer, it must be that $0=10c\ mod\ 15$.
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