Published 1972
| public
Journal Article
Open
The diophantine problem Y² - X³ = A in a polynomial ring
- Creators
- Johnson, Dennis L.
Abstract
Let C[z] be the ring of polynomials in z with complex coefficients; we consider the equation Y² — X³ = A, with A[is an element of]C[z] given, and seek solutions of this with X, Y[is an element of]C[z] i.e. we treat the equation as a "polynomial diophantine" problem. We show that when A is of degree 5 or 6 and has no multiple roots, then there are exactly 240 solutions (X, Y) to the problem with deg X ≤ 2 and deg Y ≤ 3.
Additional Information
© 1972 Pacific Journal of Mathematics. Received July 15, 1971. This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration.Files
JOHpjm72.pdf
Files
(485.5 kB)
| Name | Size | Download all |
|---|---|---|
|
md5:32e37b3eaacef49e78781be0f15dce17
|
485.5 kB | Preview Download |
Additional details
- Eprint ID
- 844
- Resolver ID
- CaltechAUTHORS:JOHpjm72
- Created
-
2005-10-19Created from EPrint's datestamp field
- Updated
-
2019-10-02Created from EPrint's last_modified field