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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Perfect parallelepipeds exist
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by Jorge F. Sawyer and Clifford A. Reiter PDF
Math. Comp. 80 (2011), 1037-1040 Request permission

Abstract:

There are parallelepipeds with edge lengths, face diagonal lengths and body diagonal lengths that are all positive integers. In particular, there is a parallelepiped with edge lengths $271$, $106$, $103$, minor face diagonal lengths $101$, $266$, $255$, major face diagonal lengths $183$, $312$, $323$, and body diagonal lengths $374$, $300$, $278$, $272$. Focused brute force searches give dozens of primitive perfect parallelepipeds. Examples include parallellepipeds with up to two rectangular faces.
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Additional Information
  • Jorge F. Sawyer
  • Affiliation: Box 8681 Farinon Center, Lafayette College, Easton, Pennsylvania 18042
  • Email: sawyerj@lafayette.edu
  • Clifford A. Reiter
  • Affiliation: Department of Mathematics, Lafayette College, Easton, Pennsylvania 18042
  • Email: reiterc@lafayette.edu
  • Received by editor(s): November 16, 2009
  • Received by editor(s) in revised form: December 3, 2009
  • Published electronically: August 17, 2010
  • Additional Notes: The support of a Lafayette EXCEL grant is appreciated
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 80 (2011), 1037-1040
  • MSC (2010): Primary 11D09
  • DOI: https://doi.org/10.1090/S0025-5718-2010-02400-7
  • MathSciNet review: 2772108