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.
The Rational Box
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