Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms
Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms. The case of quartic equations
Solving elliptic diophantine equations: the general cubic case
Solving linear systems of equations over integers with Gröbner bases
We introduce a novel application of Gröbner bases to solve (non-homogeneous) systems of integer linear equations over integers. For this purpose, we present a new algorithm which ascertains whether a linear system of equations has an integer solution or not; in the affirmative case, the general integer solution of the system is determined.
Solving parametrized systems of Pell equations
Solving the equation x3 - y2 = r in number fields.
Some applications of Baker's sharpened bounds to diophantine equations
Some applications of decomposable form equations to resultant equations
1. Introduction. The purpose of this paper is to establish some general finiteness results (cf. Theorems 1 and 2) for resultant equations over an arbitrary finitely generated integral domain R over ℤ. Our Theorems 1 and 2 improve and generalize some results of Wirsing [25], Fujiwara [6], Schmidt [21] and Schlickewei [17] concerning resultant equations over ℤ. Theorems 1 and 2 are consequences of a finiteness result (cf. Theorem 3) on decomposable form equations over R. Some applications of Theorems...
Some aspects of Davenport's work
Some bases of the Stickelberger ideal
Some classes of Diophantine equations connected with McFarland's and Ma's conjectures
In this paper we consider some special classes of Diophantine equations connected with McFarland's and Ma's conjectures about difference sets in abelian groups and we obtain an extension of known results.
Some Diophantine equations of the form .
Some diophantine equations of the form
Some diophantine equations solvable by identities
Some diophantine equations with many solutions
Some estimates for diagonal equations over p-adic fields
Some Examples of Weber-Hecke Ring Class Field Theory.
Some experimental results on the Frobenius problem.
Some extensions and refinements of a theorem of Sylvester
Some fourth degree Diophantine equations in Gaussian integers.