Add to ORKGAbstract. In this paper, we present a new technique for determining all perfect powers in so-called Pell sequences. To be precise, given a positive nonsquare integer D, we show how to (practically) solve Diophantine equations of the form x2 −Dy2n = 1 in integers x, y and n ≥ 2. Our method relies upon Frey curves and corre-sponding Galois representations and eschews lower bounds for linear forms in logarithms. Along the way, we sharpen and generalize work of Cao, Af Ekenstam, Ljunggren and Tartakowsky on these and related questions. 1
This paper is an investigation of Pell Equations-equations of the form x2 - dy2 = k where d is a non...
AbstractWe prove that there are only finitely many terms of a non-degenerate linear recurrence seque...
If a and b are distinct positive integers then a previous result of the author implies that the simu...
n=0 is given by the recurrence un = 2un−1 + un−2 with initial condition u0 = 0, u1 = 1 and its assoc...
We prove that there are only finitely many terms of a non-degenerate linear recurrence sequence whic...
AbstractWe prove that there are only finitely many terms of a non-degenerate linear recurrence seque...
We show how the Gelfond-Baker theory and diophantine approximation techniques can be applied to solv...
We show how the Gelfond-Baker theory and diophantine approximation techniques can be applied to solv...
We consider the equation (1) ax 2 by2 c 0, with a,b * and c *. It is a generalization of the Pell’s...
In this paper, we show that if (X_n, Y_n) is the nth solution of the Pell equation X^2−dY^2= ±1 for ...
In Part I the diophantine equation [formula] was studied, where [formula] is a linear binary recurre...
In Part I the diophantine equation [formula] was studied, where [formula] is a linear binary recurre...
AbstractLet A, B, G0, G1 be integers, and Gn = AGn − 1 − BGn − 2 for n ≥ 2. Let further S be the set...
Using the theory of Pellian equations, we show that the Diophantine equations have infi...
Let n be an integer. A set of positive integers {a_1, a_2,...,a_m} is said to have the property of D...
This paper is an investigation of Pell Equations-equations of the form x2 - dy2 = k where d is a non...
AbstractWe prove that there are only finitely many terms of a non-degenerate linear recurrence seque...
If a and b are distinct positive integers then a previous result of the author implies that the simu...
n=0 is given by the recurrence un = 2un−1 + un−2 with initial condition u0 = 0, u1 = 1 and its assoc...
We prove that there are only finitely many terms of a non-degenerate linear recurrence sequence whic...
AbstractWe prove that there are only finitely many terms of a non-degenerate linear recurrence seque...
We show how the Gelfond-Baker theory and diophantine approximation techniques can be applied to solv...
We show how the Gelfond-Baker theory and diophantine approximation techniques can be applied to solv...
We consider the equation (1) ax 2 by2 c 0, with a,b * and c *. It is a generalization of the Pell’s...
In this paper, we show that if (X_n, Y_n) is the nth solution of the Pell equation X^2−dY^2= ±1 for ...
In Part I the diophantine equation [formula] was studied, where [formula] is a linear binary recurre...
In Part I the diophantine equation [formula] was studied, where [formula] is a linear binary recurre...
AbstractLet A, B, G0, G1 be integers, and Gn = AGn − 1 − BGn − 2 for n ≥ 2. Let further S be the set...
Using the theory of Pellian equations, we show that the Diophantine equations have infi...
Let n be an integer. A set of positive integers {a_1, a_2,...,a_m} is said to have the property of D...
This paper is an investigation of Pell Equations-equations of the form x2 - dy2 = k where d is a non...
AbstractWe prove that there are only finitely many terms of a non-degenerate linear recurrence seque...
If a and b are distinct positive integers then a previous result of the author implies that the simu...