Euler’s prime equation within the composite grid of the modular ring Z6

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
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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 Z6. 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

  1. 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.
  2. J.V. Leyendekkers & A.G. Shannon, An Extension of Euler’s Prime Generating Function. Notes on Number Theory & Discrete Mathematics. In press.

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Cite this paper

APA

Leyendekkers, J. V., and Shannon, A. G. (2004). Euler’s prime equation within the composite grid of the modular ring Z6, Notes on Number Theory and Discrete Mathematics, 10(3), 72-76.

Chicago

Leyendekkers, JV, and AG Shannon. “Euler’s Prime Equation within the Composite Grid of the Modular Ring Z6.” Notes on Number Theory and Discrete Mathematics, 10, no. 3 (2004): 72-76.

MLA

Leyendekkers, JV, and AG Shannon. “Euler’s Prime Equation within the Composite Grid of the Modular Ring Z6.” Notes on Number Theory and Discrete Mathematics, 10.3 (2004): 72-76. Print.

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