Add to ORKGWe consider the equation (1) ax 2 by2 c 0, with a,b * and c *. It is a generalization of the Pell’s equation: x2 Dy2 1. Here, we show that: if the equation has an integer solution and a b is not a perfect square, then (1) has an infinitude of integer solutions; in this case we find a closed expression for (xn,yn) , the general positive integer solution, by an original method. More, we generalize it for any Diophantine equation of second degree and with two unknowns
Let k, t, d be arbitrary integers with k ≥ 2, t ≥ 0 and d = k2 - k. In the first section we give som...
This paper is an investigation of Pell Equations-equations of the form x2 - dy2 = k where d is a non...
In this study, we determine when the Diophantine equation x (2)-kxy+y (2)-2 (n) = 0 has an infinite ...
It is a generalization of the Pell’s equation. Here, we show that: if the equation has an integer so...
AbstractIn this paper we give some necessary conditions satisfied by the integer solutions of the Di...
Abstract: In this note we present a method of solving this Diophantine equation, method which is dif...
Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this pap...
AbstractFor any positive integer n we state and prove formulas for the number of solutions, in integ...
Includes bibliographical references (page 33)An equation which contains two or more variables and sa...
Using the theory of Pellian equations, we show that the Diophantine equations have infi...
AbstractWe prove that the Diophantine equation x2−kxy+y2+lx=0,l∈{1,2,4} has an infinite number of po...
In this paper, we determine when the equation in the title has an infinite number of positive intege...
If a and b are distinct positive integers then a previous result of the author implies that the simu...
By using the theory of Pell equations, we prove that the Diophantine equation $(x+y+z)^2=xyw$ has in...
Abstract. Let p denote a prime number. P. Samuel recently solved the problem of determining all squa...
Let k, t, d be arbitrary integers with k ≥ 2, t ≥ 0 and d = k2 - k. In the first section we give som...
This paper is an investigation of Pell Equations-equations of the form x2 - dy2 = k where d is a non...
In this study, we determine when the Diophantine equation x (2)-kxy+y (2)-2 (n) = 0 has an infinite ...
It is a generalization of the Pell’s equation. Here, we show that: if the equation has an integer so...
AbstractIn this paper we give some necessary conditions satisfied by the integer solutions of the Di...
Abstract: In this note we present a method of solving this Diophantine equation, method which is dif...
Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this pap...
AbstractFor any positive integer n we state and prove formulas for the number of solutions, in integ...
Includes bibliographical references (page 33)An equation which contains two or more variables and sa...
Using the theory of Pellian equations, we show that the Diophantine equations have infi...
AbstractWe prove that the Diophantine equation x2−kxy+y2+lx=0,l∈{1,2,4} has an infinite number of po...
In this paper, we determine when the equation in the title has an infinite number of positive intege...
If a and b are distinct positive integers then a previous result of the author implies that the simu...
By using the theory of Pell equations, we prove that the Diophantine equation $(x+y+z)^2=xyw$ has in...
Abstract. Let p denote a prime number. P. Samuel recently solved the problem of determining all squa...
Let k, t, d be arbitrary integers with k ≥ 2, t ≥ 0 and d = k2 - k. In the first section we give som...
This paper is an investigation of Pell Equations-equations of the form x2 - dy2 = k where d is a non...
In this study, we determine when the Diophantine equation x (2)-kxy+y (2)-2 (n) = 0 has an infinite ...