Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 6 - Section 6.2 - The Pigeonhole Principle - Exercises - Page 405: 6

Answer

Among a group $d+1$ integers there are at least 2 integers with exactly the same remainder when divided by $d$.

Work Step by Step

The remainder when divided by integer $d$ will be of type {0,1,2,3,....,d-1} We can see the number of possible remainders when divisor is $d$ will be d. So, according to pigeonhole principle, among a group of $d+1$ integers there are two integers with same remainder when divided by $d$.
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