This paper will discuss the solutions on the simultaneous Pell equations x2 − my2 = 1 and y2 − 11z2 = 1 where m is square free. By looking at the pattern of the solutions, some theorems will be developed. The solutions to these simultaneous equations are (x, y, z, m) = (50i − 1, 10, 3, mi) and (50i + 1, 10, 3, mi) for some expressions of mi where i is natural number
Abstract: We define a sequence of squarefree positive integers which arise naturally in the context ...
Pell equation (alternatively called the Pell- Fermat equation) is a type of a Diophantine equation o...
Recently, Chappelon and Ram\'{\i}rez Alfons\'{\i}n defined the \emph{square Frobenius number} of cop...
This paper will discuss the solutions on the simultaneous Pell equations yl ? 1yl = 1 and yl ? where...
Pell equation is a special type of Diophantine equations of the form x2 − my2 = 1, where m is a posi...
Let m be a positive integer, and let p be an odd prime. By using certain properties of Pell and quar...
If a and b are distinct positive integers then a previous result of the author implies that the simu...
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...
where p is prime and a > 1. Assuming the solutions of the Pell equation x(2) -(a(2) - 1) y(2) = 1 ar...
On integer solutions to x2 − dy2 = 1, z2 − 2dy2 = 1 by P. G. Walsh (Ottawa, Ont.) 1. Introduction. L...
Abstract. In this paper, we completely solve the simultaneous Diophantine equations x2 − az2 = 1, y2...
This paper is an investigation of Pell Equations-equations of the form x2 - dy2 = k where d is a non...
Let k, t, d be arbitrary integers with k ≥ 2, t ≥ 0 and d = k2 - k. In the first section we give som...
Abstract: We define a sequence of squarefree positive integers which arise naturally in the context ...
Pell equation (alternatively called the Pell- Fermat equation) is a type of a Diophantine equation o...
Recently, Chappelon and Ram\'{\i}rez Alfons\'{\i}n defined the \emph{square Frobenius number} of cop...
This paper will discuss the solutions on the simultaneous Pell equations yl ? 1yl = 1 and yl ? where...
Pell equation is a special type of Diophantine equations of the form x2 − my2 = 1, where m is a posi...
Let m be a positive integer, and let p be an odd prime. By using certain properties of Pell and quar...
If a and b are distinct positive integers then a previous result of the author implies that the simu...
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...
where p is prime and a > 1. Assuming the solutions of the Pell equation x(2) -(a(2) - 1) y(2) = 1 ar...
On integer solutions to x2 − dy2 = 1, z2 − 2dy2 = 1 by P. G. Walsh (Ottawa, Ont.) 1. Introduction. L...
Abstract. In this paper, we completely solve the simultaneous Diophantine equations x2 − az2 = 1, y2...
This paper is an investigation of Pell Equations-equations of the form x2 - dy2 = k where d is a non...
Let k, t, d be arbitrary integers with k ≥ 2, t ≥ 0 and d = k2 - k. In the first section we give som...
Abstract: We define a sequence of squarefree positive integers which arise naturally in the context ...
Pell equation (alternatively called the Pell- Fermat equation) is a type of a Diophantine equation o...
Recently, Chappelon and Ram\'{\i}rez Alfons\'{\i}n defined the \emph{square Frobenius number} of cop...
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