If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?
I. k + t + 2
II. k^2 + 2kt + t^2
III. k^2 + t^2	Choose the correct answer:  A) None  B) I only  C) II only  D) III only  E) I, II, and III
k^2–t^2 is an odd integer means that either k is even and t is odd or k is odd and t is even.   Check all options:   I. k + t + 2 --&gt; even+odd+even=odd or odd+even+even=odd. Discard;   II. k^2 + 2kt + t^2 --&gt; even+even+odd=odd or odd+even+even=odd. Discard;   III. k^2 + t^2 --&gt; even+odd=odd or odd+even=odd. Discard.   Nonenswer: None.
<result>A</result>
If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?
I. k + t + 2
II. k^2 + 2kt + t^2
III. k^2 + t^2