Vol. 43, No. 1, 1972

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ISSN: 0030-8730
The diophantine problem Y 2 X3 = A in a polynomial ring

Dennis Lee Johnson

Vol. 43 (1972), No. 1, 151–155
Abstract

Let C[z] be the ring of polynomials in z with complex coefficients; we consider the equation Y 2 X3 = A, with A C[z] given, and seek solutions of this with X,Y 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.

Mathematical Subject Classification 2000
Primary: 10B15
Secondary: 14H30, 12A20
Milestones
Received: 15 July 1971
Published: 1 October 1972
Authors
Dennis Lee Johnson