J. V. Leyendekkers and A. G. Shannon

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 10, 2004, Number 1, Pages 1—11

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## Details

### Authors and affiliations

J. V. Leyendekkers

*The University of Sydney, 2006 Australia*

A. G. Shannon

*Warrane College, Kensington, NSW 1465,
& KvB Institute of Technology, North Sydney, NSW 2060, Australia *

### Abstract

Modular-ring row structures are developed for squares. In particular, the row structures of even squares within the modular ring Z_{6} are analysed. This structure is shown to be linked via generalized pentagonal numbers to that of the odd squares. When 3 | *N*, the link is via the triangular numbers. Equations could thus be developed for the rows of those primes that equal a sum of squares. Since the results are general they can be used to study in some depth those systems that have squares as a dominant feature.

### AMS Classification

- 11A41
- 11A99

### References

- J.V. Leyendekkers & A.G. Shannon, Powers as a Difference of Squares: The

Effect on Triples. Notes on Number Theory & Discrete Mathematics. 8(3) 2002:

95-106. - J.V. Leyendekkers, J.M. Rybak & A.G. Shannon, The Characteristics of Primes

and Other Integers within the Modular Ring Z_{4}and in Class ̅1_{4}. Notes on

Number Theory & Discrete Mathematics. 4(1) 1998: 1-17. - J.V. Leyendekkers & A.G. Shannon, Some Characteristics of Primes within

Modular Rings. Notes on Number Theory & Discrete Mathematics. In press. - A.G. Shannon & A.F. Horadam, Generalized Fibonacci Number Triples,

American Mathematical Monthly, 80(2) 1973: 187-190.

## Related papers

## Cite this paper

APALeyendekkers, J. V., and Shannon, A. G. (2004). The row structure of squares in modular rings. Notes on Number Theory and Discrete Mathematics, 10(1), 1-11.

ChicagoLeyendekkers, JV, and AG Shannon. “The Row Structure of Squares in Modular Rings.” Notes on Number Theory and Discrete Mathematics 10, no. 1 (2004): 1-11.

MLALeyendekkers, JV, and AG Shannon. “The Row Structure of Squares in Modular Rings.” Notes on Number Theory and Discrete Mathematics 10.1 (2004): 1-11. Print.