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 4.1 - Page 163: 55


This is false. Consider the number $7$.

Work Step by Step

Consider the number $7$. The only squares smaller than it are 1 and 4. It is impossible to add $3$ or fewer of these and get $7$. To see this, first note that there must be exactly $1$ $4$ -- if there are more, the sum will be too high, and if there are less, the sum will be too low. Then, the highest that can be madei s $4+1+1 = 6$, so it is impossible and the statement is proven false.
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