10. Which of these integers cannot be expressed as the difference of two squares?
A 5
B 7
C 8
D 9
E 10
10. E The difference of two squares $a^{2}-b^{2}$ factorises to $(a+b)(a-b)$. Therefore for it to be possible to express an integer as the difference of two squares, it must be possible to factorise the integer in the form $(a+b)(a-b)$, where $a$ and $b$ are both integers. Note that $5=(3+2)(3-2) ; 7=(4+3)(4-3) ; 8=(3+1)(3-1) ; 9=(5+4)(5-4)$. So $5,7,8,9$ can all be written as the difference of two squares.
(It is left to the reader to show that 10 cannot be the difference of two squares as it cannot be written in the form $(a+b)(a-b)$ where $a$ and $b$ are both integers.)