MathDB
Triangles with integer area

Source: 2009 AIME I #11

March 18, 2009
geometryanalytic geometryvectorcalculusintegrationabsolute valueAMC

Problem Statement

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