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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


An infinite family of perfect parallelepipeds
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by Benjamin D. Sokolowsky, Amy G. VanHooft, Rachel M. Volkert and Clifford A. Reiter PDF
Math. Comp. 83 (2014), 2441-2454 Request permission


A perfect parallelepiped has edges, face diagonals, and body diagonals all of integer length. We prove the existence of an infinite family of dissimilar perfect parallelepipeds with two nonparallel rectangular faces. We also show that we can obtain perfect parallelepipeds of this form with the angle of the nonrectangular face arbitrarily close to $90^{\circ }$. Finally, we discuss the implications that this family has on the famous open problem concerning the existence of a perfect cuboid. This leads to two conjectures that would imply no perfect cuboid exists.
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Additional Information
  • Benjamin D. Sokolowsky
  • Affiliation: Bucknell University, 211 Trowbridge Lane, Downingtown, Pennsylvania 19335
  • Address at time of publication: 450 Circle Road, West G 204F, Stony Book, New York 11790
  • Email:
  • Amy G. VanHooft
  • Affiliation: The College at Brockport, State University of New York, 482 West Avenue, Brockport, New York 14420
  • Email:
  • Rachel M. Volkert
  • Affiliation: University of Northern Iowa, 315 North Guilford Street, Sumner, Iowa 50674
  • Email:
  • Clifford A. Reiter
  • Affiliation: Lafayette College, Department of Mathematics, Easton, Pennsylvania 18042
  • Email:
  • Received by editor(s): August 9, 2012
  • Received by editor(s) in revised form: December 27, 2012
  • Published electronically: November 18, 2013
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 2441-2454
  • MSC (2010): Primary 11D09
  • DOI:
  • MathSciNet review: 3223340