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
Modular-ring row structures are developed for squares. In particular, the row structures of even squares within the modular ring Z6 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.
- 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:
- J.V. Leyendekkers, J.M. Rybak & A.G. Shannon, The Characteristics of Primes
and Other Integers within the Modular Ring Z4 and in Class ̅14. 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.
Cite this paper
Leyendekkers, 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.