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
Full paper (PDF, 165 Kb)

Details

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 P_n (24T_n + 1) in which P_n, T_n 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

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