2015 AMC 10A Problem 20

A rectangle with positive integer side lengths in \text{cm} has area A \text{cm}^2 and perimeter P \text{cm}. Which of the following numbers cannot equal A+P?

\textbf{(A) }100\qquad\textbf{(B) }102\qquad\textbf{(C) }104\qquad\textbf{(D) }106\qquad\textbf{(E) }108

Note: As it originally appeared in the AMC 10, this problem was stated incorrectly and had no answer; it has been modified here to be solvable. This is the original question:

A rectangle with side lengths in \text{cm} has an area of integer A \text{cm}^2 and a perimeter of integer P \text{cm}. Which of the following numbers cannot equal A+P?

\textbf{(A) }100\qquad\textbf{(B) }102\qquad\textbf{(C) }104\qquad\textbf{(D) }106\qquad\textbf{(E) }108

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