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The diophantine problem Y² - X³ = A in a polynomial ring

Johnson, Dennis L. (1972) The diophantine problem Y² - X³ = A in a polynomial ring. Pacific Journal of Mathematics, 43 (1). pp. 151-155. ISSN 0030-8730. http://resolver.caltech.edu/CaltechAUTHORS:JOHpjm72

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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.


Item Type:Article
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.
Record Number:CaltechAUTHORS:JOHpjm72
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:JOHpjm72
Alternative URL:http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.pjm/1102959650
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:844
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:19 Oct 2005
Last Modified:26 Dec 2012 08:41

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