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
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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.