2009 AIME I Problem 11

Consider the set of all triangles OPQ where O is the origin and P and Q are distinct points in the plane with nonnegative integer coordinates (x,y) such that 41x + y = 2009. Find the number of such distinct triangles whose area is a positive integer.

Leading zeroes must be inputted, so if your answer is 34, then input 034

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