1986 AJHSME Problem 17

Let \text{o} be an odd whole number and let \text{n} be any whole number. Which of the following statements about the whole number (\text{o}^2+\text{no}) is always true?

\text{(A)}\ \text{it is always odd} \qquad \text{(B)}\ \text{it is always even}

\text{(C)}\ \text{it is even only if n is even} \qquad \text{(D)}\ \text{it is odd only if n is odd}

\text{(E)}\ \text{it is odd only if n is even}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.