We investigate the set of integral solutions, over a given number field, of the equation X2 − dY 2 = 1, where d denotes some non-zero integer of this field. We define an operation on this set such that it is an abelian group and determine the structure of this abelian group in terms of the number of complex and real embeddings of the number field, and the number of positive embeddings of d
The purpose of this paper is to develop a method for finding values of N for which the equation x[sq...
Abstract: We define a sequence of squarefree positive integers which arise naturally in the context ...
AbstractThe polynomial Pell's equation is X2−DY2=1, where D is a polynomial with integer coefficient...
Let p be a prime number such that p ≡ 1(mod 4), say p = 1+4k for a positive integer k. Let P = 2k + ...
On integer solutions to x2 − dy2 = 1, z2 − 2dy2 = 1 by P. G. Walsh (Ottawa, Ont.) 1. Introduction. L...
This paper is an investigation of Pell Equations-equations of the form x2 - dy2 = k where d is a non...
summary:We shall describe how to construct a fundamental solution for the Pell equation $x^2-my^2=1$...
Solving Pell’s equation is of relevance in finding fundamental units in real quadratic fields and fo...
AbstractIt is proved that ifaandbare different non-zero rational integers then the “simultaneous Pel...
AbstractThe following problem was posed by Dipendra Prasad. Characterize number fields K for which t...
This paper is devoted to finding integral solutions of algebraic equations. Only algebraic equation...
Let the smallest non-trivial solution of Pell equation, x^2-Dy^2=1, be denoted by (x_1, y_1). The Pe...
Pell equation (alternatively called the Pell- Fermat equation) is a type of a Diophantine equation o...
AbstractIn this paper we consider arithmetic progressions on Pell equations, i.e. integral solutions...
Let p be a prime number such that p equivalent to 1, 3(mod 4), let F-p, be a finite field, let N is ...
The purpose of this paper is to develop a method for finding values of N for which the equation x[sq...
Abstract: We define a sequence of squarefree positive integers which arise naturally in the context ...
AbstractThe polynomial Pell's equation is X2−DY2=1, where D is a polynomial with integer coefficient...
Let p be a prime number such that p ≡ 1(mod 4), say p = 1+4k for a positive integer k. Let P = 2k + ...
On integer solutions to x2 − dy2 = 1, z2 − 2dy2 = 1 by P. G. Walsh (Ottawa, Ont.) 1. Introduction. L...
This paper is an investigation of Pell Equations-equations of the form x2 - dy2 = k where d is a non...
summary:We shall describe how to construct a fundamental solution for the Pell equation $x^2-my^2=1$...
Solving Pell’s equation is of relevance in finding fundamental units in real quadratic fields and fo...
AbstractIt is proved that ifaandbare different non-zero rational integers then the “simultaneous Pel...
AbstractThe following problem was posed by Dipendra Prasad. Characterize number fields K for which t...
This paper is devoted to finding integral solutions of algebraic equations. Only algebraic equation...
Let the smallest non-trivial solution of Pell equation, x^2-Dy^2=1, be denoted by (x_1, y_1). The Pe...
Pell equation (alternatively called the Pell- Fermat equation) is a type of a Diophantine equation o...
AbstractIn this paper we consider arithmetic progressions on Pell equations, i.e. integral solutions...
Let p be a prime number such that p equivalent to 1, 3(mod 4), let F-p, be a finite field, let N is ...
The purpose of this paper is to develop a method for finding values of N for which the equation x[sq...
Abstract: We define a sequence of squarefree positive integers which arise naturally in the context ...
AbstractThe polynomial Pell's equation is X2−DY2=1, where D is a polynomial with integer coefficient...
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