# 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.

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.