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area of triangle with lattice points inside triangle and on the sides

Source: 1967 Swedish Mathematical Competition p6

March 21, 2021
geometrylatticecombinatorial geometrytriangle area

Problem Statement

The vertices of a triangle are lattice points. There are no lattice points on the sides (apart from the vertices) and nn lattice points inside the triangle. Show that its area is n+12n + \frac12. Find the formula for the general case where there are also mm lattice points on the sides (apart from the vertices).