Pell equation is a special type of Diophantine equations of the form x2 − my2 = 1, where m is a positive non-square integer. Since m is not a perfect square, then there exist infinitely many integer solutions (x, y) to the Pell equation. This paper will discuss the integral solutions to the simultaneous Pell equations x2 − my2 = 1 and y2 − pz2 = 1, where m is square free integer and p is odd prime. The solutions of these simultaneous equations are of the form of (x, y, z, m) = (yn2t±1, yn, zn, yn2t2±2t) and (y2n/2 t ±1, yn, zn, y2n/4 t2) for yn odd and even respectively, where t ∈ N
This paper is an investigation of Pell Equations-equations of the form x2 - dy2 = k where d is a non...
On integer solutions to x2 − dy2 = 1, z2 − 2dy2 = 1 by P. G. Walsh (Ottawa, Ont.) 1. Introduction. L...
Let $ \{P_{n}\}_{n\geq 0} $ be the sequence of Padovan numbers defined by $ P_0=0 $, $ P_1 = P_2=1$...
This paper will discuss the solutions on the simultaneous Pell equations x2 − my2 = 1 and y2 − 11z2 ...
Let m be a positive integer, and let p be an odd prime. By using certain properties of Pell and quar...
WOS: 000380694300011Let be an integer and p prime number. It is well-known that the solutions of the...
In this paper, we consider the simultaneous Pell equations $ (a^2+1)y^2-x^2 = y^2-bz^2 = 1 $ where $...
AbstractIt is proved that ifaandbare different non-zero rational integers then the “simultaneous Pel...
In this paper, we show that if (Xk,Yk) is the kth solution of the Pell equation X2-dY2=1 for some no...
It is important in techniques of drawing to find combinations of the slopes of two straight lines an...
If a and b are distinct positive integers then a previous result of the author implies that the simu...
This paper will discuss the solutions on the simultaneous Pell equations yl ? 1yl = 1 and yl ? where...
where p is prime and a > 1. Assuming the solutions of the Pell equation x(2) -(a(2) - 1) y(2) = 1 ar...
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 ...
Pell equation (alternatively called the Pell- Fermat equation) is a type of a Diophantine equation o...
This paper is an investigation of Pell Equations-equations of the form x2 - dy2 = k where d is a non...
On integer solutions to x2 − dy2 = 1, z2 − 2dy2 = 1 by P. G. Walsh (Ottawa, Ont.) 1. Introduction. L...
Let $ \{P_{n}\}_{n\geq 0} $ be the sequence of Padovan numbers defined by $ P_0=0 $, $ P_1 = P_2=1$...
This paper will discuss the solutions on the simultaneous Pell equations x2 − my2 = 1 and y2 − 11z2 ...
Let m be a positive integer, and let p be an odd prime. By using certain properties of Pell and quar...
WOS: 000380694300011Let be an integer and p prime number. It is well-known that the solutions of the...
In this paper, we consider the simultaneous Pell equations $ (a^2+1)y^2-x^2 = y^2-bz^2 = 1 $ where $...
AbstractIt is proved that ifaandbare different non-zero rational integers then the “simultaneous Pel...
In this paper, we show that if (Xk,Yk) is the kth solution of the Pell equation X2-dY2=1 for some no...
It is important in techniques of drawing to find combinations of the slopes of two straight lines an...
If a and b are distinct positive integers then a previous result of the author implies that the simu...
This paper will discuss the solutions on the simultaneous Pell equations yl ? 1yl = 1 and yl ? where...
where p is prime and a > 1. Assuming the solutions of the Pell equation x(2) -(a(2) - 1) y(2) = 1 ar...
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 ...
Pell equation (alternatively called the Pell- Fermat equation) is a type of a Diophantine equation o...
This paper is an investigation of Pell Equations-equations of the form x2 - dy2 = k where d is a non...
On integer solutions to x2 − dy2 = 1, z2 − 2dy2 = 1 by P. G. Walsh (Ottawa, Ont.) 1. Introduction. L...
Let $ \{P_{n}\}_{n\geq 0} $ be the sequence of Padovan numbers defined by $ P_0=0 $, $ P_1 = P_2=1$...