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Original scientific paper

On a certain family of quartic Thue equations with three parameters

Volker Ziegler


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Abstract

We consider the parameterized Thue equation

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

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

Keywords

Diophantine equations; parameterized Thue equations; norm form equations; simultaneous Pellian equations

Hrčak ID:

3295

URI

https://hrcak.srce.hr/3295

Publication date:

24.5.2006.

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