The three vertices of a triangle are lattice points. The triangle contains no other lattice points but its interior contains exactly one lattice point.

Prove that the interior lattice point is the triangle's centroid.

(In reply to re(2): One Solution (spoiler) by Jer)

As implied from Jer's post, there are an infinite number of additional scalene triangles that can have all three vertices as lattice points with a single lattice point in its interior. These triangles will have side lengths of
SQRT(m²+1);
SQRT(n²+1); and
SQRT((m+n)²+2)
where m and n are different integers.

Posted by Dej Mar on 2011-04-11 16:17:55