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

Answer

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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.