Solving algebraic equations with Integer Structure Analysis

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 18, 2012, Number 4, Pages 54–60
Full paper (PDF, 100Kb

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Authors and affiliations

J. V. Leyendekkers

Faculty of Science, The University of Sydney
Sydney, NSW 2006, Australia

A. G. Shannon

Faculty of Engineering & IT, University of Technology
Sydney, NSW 2007, Australia

Abstract

A new alternative method for solving algebraic equations is expounded. Integer Structure Analysis is used with an emphasis on parity, right-end-digits of the components and
the modular ring Z₅.

Keywords

• Modular rings
• Quadratic equations
• Cubic equations
• Simultaneous equations
• Complex roots
• Integer structure analysis

AMS Classification

• 11A07.

References

1. Hall, H. S., S. R. Knight. 1952. Elementary Algebra. London: Macmillan.
2. Horadam, A. F., A. G. Shannon. 1988. Asveld’s polynomials. In A. N. Philippou, A. F. Horadam, G. E. Bergum (eds), Applications of Fibonacci Numbers. Dordrecht: Kluwer, 163–176.
3. Lee, T. 1994. Advanced Mathematics. 3rd edition. Fairfield, NSW: T.Lee.
4. Leyendekkers, J. V., A. G. Shannon. The Cardano Family of Cubics . Notes on Number Theory and Discrete Mathematics, Vol. 5, 1999, No. 4, 151–162.
5. Leyendekkers, J. V., A. G. Shannon. Analysis of the Roots of Some Cardano Cubes . Notes on Number Theory and Discrete Mathematics, Vol. 6, 1999, No. 4, 113–117.
6. Leyendekkers, J. V., A. G. Shannon, J. M. Rybak. 2007. Pattern Recognition: Modular Rings and Integer Structure. North Sydney: Raffles KvB Monograph No 9.