Add to ORKGAbstract. We give conditions on the rational numbers a, b, c which imply that there are infinitely many triples (x, y, z) of rational numbers such that x+ y + z = a+ b+ c and xyz = abc. We do the same for th
Set of m positive integers is called a Diophantine m-tuple if the product of its any two distinct el...
AbstractThe wealth of Pythagorean number triples is demonstrated afresh by showing that for every ra...
In this article, we construct families of elliptic curves arising from the Heron triangles and Diop...
We study the Diophantine system{ x1 + · · ·+ xn = a, x3 1 + · · ·+ x3n = b, where a, b ∈ Q, ab 6 =...
A rational Diophantine triple is a set of three nonzero rational (a,b,c) with the property that $ab+...
We show that for infinitely many square-free integers q there exist infinitely many triples of ratio...
Rational Diophantine triples, i.e. rationals a, b, c with the property that ab + 1, ac + 1, bc + 1 a...
Let C be a smooth genus one curve described by a quartic polynomial equation over the rational field...
textabstractIn this paper the family of elliptic curves over Q given by the equation y2 = (x + p)(x2...
AbstractWe establish a relationship between the rational solutions (X(t), Y(t)) over K(t), K the alg...
summary:We consider a variety of Euler's sum of powers conjecture, i.e., whether the Diophantine sys...
In this paper the family of elliptic curves over Q given by the equation y(2) = (x + p)(x(2) + p(2))...
Some arithmetic of elliptic curves and theory of elliptic surfaces is used to find all rational solu...
Given an equation of the form f(x, y) = 0, where f is a polynomial in two variables with rational co...
Let K be a number field and E be an elliptic curve described by the Weierstrass equation over K. As ...
Set of m positive integers is called a Diophantine m-tuple if the product of its any two distinct el...
AbstractThe wealth of Pythagorean number triples is demonstrated afresh by showing that for every ra...
In this article, we construct families of elliptic curves arising from the Heron triangles and Diop...
We study the Diophantine system{ x1 + · · ·+ xn = a, x3 1 + · · ·+ x3n = b, where a, b ∈ Q, ab 6 =...
A rational Diophantine triple is a set of three nonzero rational (a,b,c) with the property that $ab+...
We show that for infinitely many square-free integers q there exist infinitely many triples of ratio...
Rational Diophantine triples, i.e. rationals a, b, c with the property that ab + 1, ac + 1, bc + 1 a...
Let C be a smooth genus one curve described by a quartic polynomial equation over the rational field...
textabstractIn this paper the family of elliptic curves over Q given by the equation y2 = (x + p)(x2...
AbstractWe establish a relationship between the rational solutions (X(t), Y(t)) over K(t), K the alg...
summary:We consider a variety of Euler's sum of powers conjecture, i.e., whether the Diophantine sys...
In this paper the family of elliptic curves over Q given by the equation y(2) = (x + p)(x(2) + p(2))...
Some arithmetic of elliptic curves and theory of elliptic surfaces is used to find all rational solu...
Given an equation of the form f(x, y) = 0, where f is a polynomial in two variables with rational co...
Let K be a number field and E be an elliptic curve described by the Weierstrass equation over K. As ...
Set of m positive integers is called a Diophantine m-tuple if the product of its any two distinct el...
AbstractThe wealth of Pythagorean number triples is demonstrated afresh by showing that for every ra...
In this article, we construct families of elliptic curves arising from the Heron triangles and Diop...