15-Jan-1995

Unsolved Problem 3:

Does there exist a rectangular box all of whose edges and diagonals are integers?

By a rectangular box, we mean a solid with six rectangular faces. This common figure is also known as a rectangular parallelepiped.
The diagonals of a box include the face diagonals and the main diagonals.
A face diagonal joins opposite vertices of a face.
A main diagonal (or space diagonal) joins opposite vertices of the box.

Reference:

[Ogilvy 1972]
C. Stanley Ogilvy, Tomorrow's Math: Unsolved Problems for the Amateur. 2nd edition. Oxford University Press. New York: 1972. Page 120.
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