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On the Derived Cuboid

Published online by Cambridge University Press:  20 November 2018

W. G. Spohn
W. G. Spohn*
Affiliation:
Johns Hopkins University, Applied Physics Laboratory
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We showed in [1] that the Eulerian family of cuboids with integral edges and face diagonals did not have integral inner diagonals. We now show that the derived family does not have integral inner diagonals except possibly when the generators are divisible by 705180. In this case there appears to be no inherent reason why the diagonals cannot be integral.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 575 - 577
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Spohn, W. G., On the integral cuboid, Amer. Math. Monthly, 79 (1972) 57-59.Google Scholar
2. Lai, M. and Blundon, W. J., Solutions of the Diophantine equations x2+y2=l2, y2+z2=m2, z2+x2=n2 Math. Comp., 20 (1966) 144-147.Google Scholar
3. Kraitchik, M., Th?orie des Nombres, Tome III, Analyse Diophantine et Applications aux Cubo?des Rationnels, Gauthier-Villars, Paris, 1947.Google Scholar
4. Mordell, L. J., Diophantine Equations, Academic Press, London and New York, 1969.Google Scholar