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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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.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||19 Oct 2005|
|Last Modified:||26 Dec 2012 08:41|
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