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 4.6 - Page 206: 29

Answer

a| b means that for some integer m, b = am a ∤c means that for some integer n, c = an + x where x is any integer such that x is not divisible by a Then, (b + c)/a = (am + an + x)/a = (a(m + n)+x)/a = a(m + n)/a+ x/a = (m+n)+ x/a Since x/a is not an integer, we conclude that a ∤ (b+c) if a| b and a ∤c
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Work Step by Step

Steps: 1. Express b in terms of a by division rule (if a| b then b = am for some integer m) 2. Express c in terms of a. 3. Compute \frac{b+c}{a} by putting the value of b and c from step 1 and step 2.
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