Question

Prove or give a counterexample: Every positive integer can be expressed as the sum of three or fewer perfect squares. (A perfect square is an integer n for which there is an integer k with the property: n

Answer 1

Answer:

Statement is incorrect

Step-by-step explanation:

Every positive integer cannot be expressed as the sum of three or fewer perfect squares.

Supposing the number 7 only squares less than are 0, 1  and   4

Clearly 7 can not be written using three or fewer of these numbers

It is proved

By taking Cube root of 7

$\sqrt[3]{7}$ = 1.912931183

Now By taking  

$\sqrt{7}$ = 2.64575131

So both values 1.912931183 and 2.64575131 are not positive integers.

Hence the statement is incorrect.