1979 AHSME Problem 26

The function f satisfies the functional equation f(x) +f(y) = f(x + y ) - xy - 1 for every pair x,~ y of real numbers. If f( 1) = 1, then the number of integers n \neq 1 for which f ( n ) = n is

\textbf{(A) }0\qquad \textbf{(B) }1\qquad \textbf{(C) }2\qquad \textbf{(D) }3\qquad \textbf{(E) }\infty

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