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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## Details

### 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 *Z _{5}*.

### Keywords

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

### AMS Classification

- 11A07.

### References

- Hall, H. S., S. R. Knight. 1952. Elementary Algebra. London: Macmillan.
- 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.
- Lee, T. 1994. Advanced Mathematics. 3rd edition. Fairfield, NSW: T.Lee.
- 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.
- 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.
- Leyendekkers, J. V., A. G. Shannon, J. M. Rybak. 2007. Pattern Recognition: Modular Rings and Integer Structure. North Sydney: Raffles KvB Monograph No 9.

## Related papers

## Cite this paper

APALeyendekkers, J., & Shannon, A.(2012). Solving algebraic equations with integer structure analysis, Notes on Number Theory and Discrete Mathematics, 18(4), 54-60.

ChicagoLeyendekkers, JV, and AG Shannon. “Solving Algebraic Equations with Integer Structure Analysis.” Notes on Number Theory and Discrete Mathematics 18, no. 4 (2012): 54-60.

MLALeyendekkers, JV, and AG Shannon. “Solving Algebraic Equations with Integer Structure Analysis.” Notes on Number Theory and Discrete Mathematics 18.4 (2012): 54-60. Print.