Modular rings and the integer 3

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 17, 2011, Number 2, Pages 47–51
Full paper (PDF, 176 Kb)

Details

Authors and affiliations

J. V. Leyendekkers
The University of Sydney, 2006, Australia

A. G. Shannon
Faculty of Engineering & IT, University of Technology Sydney
2007 Australia

Abstract

The characteristics within modular rings of the integer three are discussed. This integer has unique row structures in modular rings which appear to underlie restraints on various aspects of triples, particularly the factors and powers structure of the components. The function N = x^m + 2ⁿ, with m even and n odd but x not divisible by 3, always has 3 as a factor, and a majority of elements of the sequence of triangular numbers {N_T} are such that 3|N_T. The modular ring Z₃ and the distribution of primes within its structure are also discussed.

Keywords

• Integer structure analysis
• Modular rings
• Prime numbers
• Triangular numbers
• Pentagonal numbers
• Octagonal numbers
• Repunits

AMS Classification

• 11A41
• 11A07

References

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