164 research outputs found
Integral points on a certain family of elliptic curves
The Thue-Siegel method is used to obtain an upper bound for the number of
primitive integral solutions to a family of quartic Thue's inequalities. This
will provide an upper bound for the number of integer points on a family of
elliptic curves with j-invariant equal to 1728
The Method Of Thue-Siegel For Binary Quartic Forms
We will use Thue-Siegel method, based on Pad\'e approximation via
hypergeometric functions, to give upper bounds for the number of integral
solutions to the equation as well as the inequalities , for a certain family of irreducible quartic binary forms.Comment: A version of this paper is to appear in Acta. Arit
Upper bounds for the number of solutions to quartic Thue equations
We will give upper bounds for the number of integral solutions
to quartic Thue equations. Our main tool here is a logarithmic curve (x,y) that allows us to use the theory of linear forms in logarithms. This manuscript improves the results of author's earlier work with Okazaki [2] by giving special
treatments to forms with respect to their signature
On the simplest sextic fields and related Thue equations
We consider the parametric family of sextic Thue equations where
is an integer and is a divisor of . We
show that the only solutions to the equations are the trivial ones with
.Comment: 12 pages, 2 table
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