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Rectangular parallelepipeds with at least one integer side

Source: ILL 1979 - Problem 81.

June 5, 2011
geometry unsolvedgeometry

Problem Statement

Let Π\Pi be the set of rectangular parallelepipeds that have at least one edge of integer length. If a rectangular parallelepiped P0P_0 can be decomposed into parallelepipeds P1,P2,...,PN∈ΠP_1,P_2, . . . ,P_N\in \Pi, prove that P0∈ΠP_0\in \Pi.
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