Thank you very much for this article! I’m just starting my studies, and I planned to do the same thing as your student. I’ll definitely change my studies now that I’ve read your advice 🙂

]]>In order for m and n to add to be odd, one would have to be even the other odd (logic explained in original answer).

The difference between m (p^2+4p+4) and n (p^2+6p+9)

is 2p+5…For any integer value of p (1,2,3,etc…) that value of 2p+5 between M and N will always be odd.

There is no way that the difference between 2 odd numbers or 2 even numbers will be odd, so we must be dealing with one odd and one even.

Once we know that one is odd and one is even, C is our answer.

]]>1. m = p^2 + 4p + 4

– 4p + 4 is always even

– p^2 is either odd or even

-> m is either odd or even

2. n = p^2 + 6p + 9

– 6p + 9 is always odd

– p^2 is either odd or even

-> n is either odd or even

m + n = 2.p^2 + 12p + 13

– 2.p^2 + 12p is always even

-> m + n is always odd

-> C is the answer