**J. V. Leyendekkers, A. G. Shannon and C. K. Wong**

Notes on Number Theory and Discrete Mathematics

ISSN 1310–5132

Volume 8, 2002, Number 3, Pages 85–94

**Full paper (PDF, 463 Kb)**

## Details

### Authors and affiliations

**J. V. Leyendekkers**

*The University of Sydney
NSW 2006, Australia*

**A. G. Shannon**

*Warrane College, The University of New South Wales, 1465, &
KvB Institute of Technology, North Sydney, 2060, Australia*

**C. K. Wong**

*Warrane College, The University of New South Wales,
Kensington, 1465*

### Abstract

It is shown that the functions , and intersect at a point that is always non-integer, A geometric analysis shows that the cubic crosses the x -axis at a point, x_{0}, that is always non-integer, with , where is obtained from the geometry of the curve. These results show that a general parameter associated with the real roots of Fermat/Cardano polynomials is a function of and the geometry of the curve, which in turn yield the link with the geometry of the complex plane.

### AMS Classification

- 11C08
- 11D41
- 11B37

### References

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## Cite this paper

Leyendekkers, J., Shannon, A. & Wong C. (2002). Algebraic and geometric analysis of a Fermat/Cardano cubic. *Notes on Number Theory and Discrete Mathematics*, 8(3), 85-94.