Add to ORKGAbstract. We discuss positive integer solutions to Diophantine equa-tions of the shape x(x+ 1)(x+ 2) = ny2; where n is a xed positive integer. From the by-no-means-original ob-servation that such solutions guarantee that n is a congruent number, we show that, given a positive integer m and a nonzero integer a, there exist innitely many congruent numbers in the residue class a modulo m. After sketching relationships to various classical quartic equations, we conclude with some remarks on computational problems. 1
We consider the problem of describing all non-negative integer solutions to a linear congruence in m...
By using the theory of Pell equations, we prove that the Diophantine equation $(x+y+z)^2=xyw$ has in...
Let n be an integer. A set of positive integers {a_1, a_2,...,a_m} is said to have the property of D...
Assuming the Birch and Swinnerton-Dyer conjecture, an odd square-free integer $n$ is a congruent num...
Assuming the Birch and Swinnerton-Dyer conjecture, an odd square-free integer $n$ is a congruent num...
Assuming the Birch and Swinnerton-Dyer conjecture, an odd square-free integer $n$ is a congruent num...
Assuming the Birch and Swinnerton-Dyer conjecture, an odd square-free integer $n$ is a congruent num...
Abstract. A famous problem posed by Diophantus was to nd sets of distinct positive rational numbers ...
We consider a Diophantine equation arising from a generalization of the classical Lucas problem of t...
We shall consider the following problem: Could a product of some consecutive integers be a power of ...
ABSTRACT. We consider a Diophantine equation arising from a generalization of the classical Lucas pr...
Abstract. Wilhelm Ljunggren proved many fundamental theorems on equations of the form aX2 bY 4 = , ...
For positive integers x, y, the equation x4 + (n2-2)y - z always has the trivial solution x - y. In ...
Abstract. In this paper, we prove a weaker form of a conjecture of Mohanty and Ramasamy [6] concerni...
The object of this thesis is to solve, in integers X and Y, various equations of the form [equation]...
We consider the problem of describing all non-negative integer solutions to a linear congruence in m...
By using the theory of Pell equations, we prove that the Diophantine equation $(x+y+z)^2=xyw$ has in...
Let n be an integer. A set of positive integers {a_1, a_2,...,a_m} is said to have the property of D...
Assuming the Birch and Swinnerton-Dyer conjecture, an odd square-free integer $n$ is a congruent num...
Assuming the Birch and Swinnerton-Dyer conjecture, an odd square-free integer $n$ is a congruent num...
Assuming the Birch and Swinnerton-Dyer conjecture, an odd square-free integer $n$ is a congruent num...
Assuming the Birch and Swinnerton-Dyer conjecture, an odd square-free integer $n$ is a congruent num...
Abstract. A famous problem posed by Diophantus was to nd sets of distinct positive rational numbers ...
We consider a Diophantine equation arising from a generalization of the classical Lucas problem of t...
We shall consider the following problem: Could a product of some consecutive integers be a power of ...
ABSTRACT. We consider a Diophantine equation arising from a generalization of the classical Lucas pr...
Abstract. Wilhelm Ljunggren proved many fundamental theorems on equations of the form aX2 bY 4 = , ...
For positive integers x, y, the equation x4 + (n2-2)y - z always has the trivial solution x - y. In ...
Abstract. In this paper, we prove a weaker form of a conjecture of Mohanty and Ramasamy [6] concerni...
The object of this thesis is to solve, in integers X and Y, various equations of the form [equation]...
We consider the problem of describing all non-negative integer solutions to a linear congruence in m...
By using the theory of Pell equations, we prove that the Diophantine equation $(x+y+z)^2=xyw$ has in...
Let n be an integer. A set of positive integers {a_1, a_2,...,a_m} is said to have the property of D...