Bunuel wrote:

Which of the following CANNOT be expressed as the sum of squares of two integer?

A 13

B 17

C 21

D 29

E 34

Every prime of the form (4k+1) can be expressed as the sum of two squares..

Among the answer options 13,17, and 29 are prime and they can be written in the form (4k+1). So, eliminate A,B, and D.

when the number is not prime:- If each of the factors of the integer can be written as the sum of two squares is itself expressible as the sum of two squares.Prime factorization of 34=2*17, (\(2=1^2+1^2\) & 17 is in the form of 4k+1. So, both 2 & 17 are perfect squares)

Therefore, 34 is a sum of squares of two integer.So, eliminate E.

Ans. (C)

_________________

Regards,

PKN

Rise above the storm, you will find the sunshine