On sums of multiple squares

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 18, 2012, Number 1, Pages 9—15
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Authors and affiliations

J. V. Leyendekkers

Faculty of Science, The University of Sydney
Sydney, NSW 2006, Australia

A. G. Shannon

Faculty of Engineering & IT, University of Technology
Sydney, NSW 2007, Australia


The structural and other characteristics of the Hoppenot multiple square equation are analysed in the context of the modular ring Z4. This equation yields a left-hand-side and a right-hand-side sum equal to Pn (24Tn + 1) in which Pn, Tn represent the pyramidal and triangular numbers, respectively. This sum always has 5 as a factor. Integer structure analysis is also used to solve some related problems.


  • Integer structure analysis
  • Modular rings
  • Hoppenot equation
  • Triangular numbers
  • Pentagonal numbers
  • Pyramidal numbers

AMS Classification

  • 11A07
  • 11B50


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Cite this paper

Leyendekkers, J., & Shannon, A.(2012). On sums of multiple squares, Notes on Number Theory and Discrete Mathematics, 18(1), 9-15.

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