Answer
$16$ is minimal.
Work Step by Step
There are $15$ residues mod $15$, so for the pigeonhole principle to take effect and numbers share a residue, there must be $16$ integers, as $16>15$.
Discrete Mathematics with Applications 4th Edition
by Epp, Susanna S.
Published by
Cengage Learning
ISBN 10:
0-49539-132-8
ISBN 13:
978-0-49539-132-6
Chapter 9 - Counting and Probability - Exercise Set 9.4 - Page 564: 18
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