AbstractWe present elementary necessary and sufficient conditions for the solvability of the Diophantine equation x2 − Dy2 = n for any n ∈ ℤ and any nonsquare integer D > 0, using only simple continued fraction expansions. This includes a simple device for finding fundamental solutions of such equations
AbstractFor any positive integer n we state and prove formulas for the number of solutions, in integ...
The theory of continued fractions has applications in cryptographic problems and in solution methods...
AbstractWe prove that the equation x2 − kxy + y2 + x = 0 with k ϵ N+ has an infinite number of posit...
AbstractIn this paper we give some necessary conditions satisfied by the integer solutions of the Di...
THEOREM. The equation of the title has no solutions in positive integers x, y for any value of the p...
We consider the equation (1) ax 2 by2 c 0, with a,b * and c *. It is a generalization of the Pell’s...
The study presents the theory of convergents of simple finite continued fractions and diophantine eq...
Abstract: In this note we present a method of solving this Diophantine equation, method which is dif...
The study of equations whose solutions were in integers was studied for several centuries. Tradition...
AbstractWe investigate the solutions of diophantine equations of the form dx2−d⁎y2=±t for t∈{1,2,4} ...
In this article we formalize some results of Diophantine approximation, i.e. the approximation of an...
Includes bibliographical references.The Diophantine equation, x² - Dy² = N, where D and N are known ...
We derive midpoint criteria for solving Pell's equation x-Dy = ±1, using the nearest square continue...
AbstractCertain diophantine equations of the form x2 − Dy2 = nz2 are solved parametrically. In parti...
Abstract: We consider the global generalization of the continued fraction giving the best ...
AbstractFor any positive integer n we state and prove formulas for the number of solutions, in integ...
The theory of continued fractions has applications in cryptographic problems and in solution methods...
AbstractWe prove that the equation x2 − kxy + y2 + x = 0 with k ϵ N+ has an infinite number of posit...
AbstractIn this paper we give some necessary conditions satisfied by the integer solutions of the Di...
THEOREM. The equation of the title has no solutions in positive integers x, y for any value of the p...
We consider the equation (1) ax 2 by2 c 0, with a,b * and c *. It is a generalization of the Pell’s...
The study presents the theory of convergents of simple finite continued fractions and diophantine eq...
Abstract: In this note we present a method of solving this Diophantine equation, method which is dif...
The study of equations whose solutions were in integers was studied for several centuries. Tradition...
AbstractWe investigate the solutions of diophantine equations of the form dx2−d⁎y2=±t for t∈{1,2,4} ...
In this article we formalize some results of Diophantine approximation, i.e. the approximation of an...
Includes bibliographical references.The Diophantine equation, x² - Dy² = N, where D and N are known ...
We derive midpoint criteria for solving Pell's equation x-Dy = ±1, using the nearest square continue...
AbstractCertain diophantine equations of the form x2 − Dy2 = nz2 are solved parametrically. In parti...
Abstract: We consider the global generalization of the continued fraction giving the best ...
AbstractFor any positive integer n we state and prove formulas for the number of solutions, in integ...
The theory of continued fractions has applications in cryptographic problems and in solution methods...
AbstractWe prove that the equation x2 − kxy + y2 + x = 0 with k ϵ N+ has an infinite number of posit...
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