On Lucas and Lehmer sequences and their applications to Diophantine equations
On the diophantine equation
In this paper, we find all integer solutions of the equation in the title for non-negative integers and under the condition that the integers and are relatively prime and . The proof depends on the famous primitive divisor theorem due to Bilu, Hanrot and Voutier and the computational techniques on some elliptic curves.
On the number of large integer points on elliptic curves
On the number of pairs of binary forms with given degree and given resultant
On the power-free parts of consecutive integers
On two-parametric family of quartic Thue equations
We show that for all integers and there are no non-trivial solutions of Thue equationsatisfying the additional condition .
Parametrized solutions of Diophantine equations
Solving a family of Thue equations with an application to the equation x²-Dy⁴=1
The Diophantine equation xⁿ = Dy² + 1
The method of Thue-Siegel for binary quartic forms
The Mordell-Weil bases for the elliptic curve
Let be an elliptic curve over of the form , where is an integer. In this paper we prove that the two points and on can be extended to a basis for under certain conditions described explicitly.
Thomas’ conjecture over function fields
Thomas’ conjecture is, given monic polynomials
Thue equations over algebraic function fields
Thue equations with composite fields
Using Lucas sequences to generalize a theorem of Sierpiński