Triangles with integer area
Source: 2009 AIME I #11
March 18, 2009
geometryanalytic geometryvectorcalculusintegrationabsolute valueAMC
Problem Statement
Consider the set of all triangles where is the origin and and are distinct points in the plane with nonnegative integer coordinates such that 41x\plus{}y \equal{} 2009. Find the number of such distinct triangles whose area is a positive integer.