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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## 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 Z_{4}. 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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## Cite this paper

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