TUYMAADA 1999 Problem 8
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
Dataset text AI-MO AoPS. Quoted with source.
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