Glasnik Matematicki, Vol. 41, No.1 (2006), 9-30.

ON A CERTAIN FAMILY OF QUARTIC EQUATIONS WITH THREE PARAMETERS

Volker Ziegler

Institut für Mathematik A, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria
e-mail: ziegler@finanz.math.tugraz.at

Abstract.   We consider the parameterized Thue equation

X4 - 4sX3Y - (2ab + 4(a + b)s)X2Y2 - 4absXY3 + a2b2Y4 = ± 1,

with a, b in 1/4 Z such that ab in Z. By the hypergeometric method and a method of Tzanakis we find all solutions, if s is large with respect to |a| and |b|.

2000 Mathematics Subject Classification.   11D59, 11D25, 11D09.

Key words and phrases.   Diophantine equations, parameterized Thue equations, norm form equations, simultaneous Pellian equations.

Full text (PDF) (free access)

DOI: 10.3336/gm.41.1.02

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