On a certain family of quadratic Thue equations
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Date
2006
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
GLASNIK MATEMATICKI
Abstract
We consider the parameterized Thue equation
X^4 − 4sX^3Y − (2ab + 4(a + b)s)X^2Y^2 − 4absXY^3 + a^2b^2Y^4 = ±1, with a, b ∈ 1/4Z 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|.
Description
Thue [15] who proved that Diophantine equation (1.1) has only finitely many solutions (X, Y) ∈ Z^2. The proof of this theorem is based on Thue’s approximation theorem.
Keywords
Diophantine equations, parameterized Thue equations, norm form equations, simultaneous Pellian equations
Citation
Ziegler, V. (2006). On a certain family of quadratic Thue equations with three parameters. Pg 9-30.