Tuymaada 1999, Q8
Source: Tuymaada 1999, Q8
July 31, 2012
calculusintegrationanalytic geometrygeometryparallelogramnumber theorygreatest common divisor
Problem Statement
A right parallelepiped (i.e. a parallelepiped one of whose edges is perpendicular to a face) is given. Its vertices have integral coordinates, and no other points with integral coordinates lie on its faces or edges. Prove that the volume of this parallelepiped is a sum of three perfect squares. Proposed by A. Golovanov