Glasnik matematički, Vol. 41 No. 1, 2006.
Original scientific paper
On a certain family of quartic Thue equations with three parameters
Volker Ziegler
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
Publication date:
24.5.2006.
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