J. V. Leyendekkers and A. G. Shannon

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

Volume 10, 2004, Number 3, Pages 72—76

**Download full paper: PDF, 39 Kb**

## 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

The extended Euler-prime-generating equation is shown to be compatible with the composite grid of the modular ring Z_{6}. Invalid values of the variable *x* (those *x* values which yield composites) follow regular sequences within the grid and have associated couples within the modular ring which are linked to the prime values.

### AMS Classification

- 11A41
- 11A07

### References

- A.F. Horadam & A.G. Shannon, Asveld’s Polynomials. In A.N. Philippou, A.F. Horadam & G.E. Bergum (eds), Applications of Fibonacci Numbers. Kluwer: Dordrecht, 1988, pp.163-176.
- J.V. Leyendekkers & A.G. Shannon, An Extension of Euler’s Prime Generating Function. Notes on Number Theory & Discrete Mathematics. In press.

## Related papers

## Cite this paper

APALeyendekkers, J. V., and Shannon, A. G. (2004). Euler’s prime equation within the composite grid of the modular ring Z_{6}, Notes on Number Theory and Discrete Mathematics, 10(3), 72-76.

Leyendekkers, JV, and AG Shannon. “Euler’s Prime Equation within the Composite Grid of the Modular Ring Z_{6}.” Notes on Number Theory and Discrete Mathematics, 10, no. 3 (2004): 72-76.

Leyendekkers, JV, and AG Shannon. “Euler’s Prime Equation within the Composite Grid of the Modular Ring Z_{6}.” Notes on Number Theory and Discrete Mathematics, 10.3 (2004): 72-76. Print.