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

Abstract

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.

Keywords

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

AMS Classification

  • 11A07
  • 11B50

References

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    7. Leyendekkers, J. V., A. G. Shannon. Integer Structure Analysis of the Product of Adjacent Integers and Euler’s Extension of Fermat’s Last Theorem. Advanced Studies in Contemporary Mathematics. Vol. 17, 2008, No. 2: 221–229.
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      Cite this paper

      APA

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

      Chicago

      Leyendekkers, JV, and AG Shannon. “On Sums of Multiple Squares.” Notes on Number Theory and Discrete Mathematics 18, no. 1 (2012): 9-15.

      MLA

      Leyendekkers, JV, and AG Shannon. “On Sums of Multiple Squares.” Notes on Number Theory and Discrete Mathematics 18.1 (2012): 9-15. Print.

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