The divisibility of by powers of .
Corps de nombres algébriques d'anneau d'entiers monogène
Sur les générateurs des ordres monogènes des corps de nombres algébriques.
Sur les polynômes à coefficients entiérs et de discriminant donné
On some arithmetical properties of Lucas and Lehmer numbers
Über die Verteilung der Lösungen von Normformen Gleichungen, III
Über die Verteilung der Lösungen von Normformen Gleichungen, II
On unit equations with rational coefficients
Index form equations in quintic fields
The problem of determining power integral bases in algebraic number fields is equivalent to solving the corresponding index form equations. As is known (cf. Győry [25]), every index form equation can be reduced to an equation system consisting of unit equations in two variables over the normal closure of the original field. However, the unit rank of the normal closure is usually too large for practical use. In a recent paper Győry [27] succeeded in reducing index form equations to systems of unit...
Bounds for the solutions of Thue-Mahler equations and norm form equations
Bounds for the solutions of unit equations
Bounds for the solutions of S-unit equations and decomposable form equations
On prime factors of sums of integers III
Finiteness criteria for decomposable form equations
On the equation
Index form equations in sextic fields: a hard computation
On power values of pyramidal numbers, I
Equal values of binary forms at integral points
Effective results for Diophantine equations over finitely generated domains
Let A be an arbitrary integral domain of characteristic 0 that is finitely generated over ℤ. We consider Thue equations F(x,y) = δ in x,y ∈ A, where F is a binary form with coefficients from A, and δ is a non-zero element from A, and hyper- and superelliptic equations in x,y ∈ A, where f ∈ A[X], δ ∈ A∖0 and . Under the necessary finiteness conditions we give effective upper bounds for the sizes of the solutions of the equations in terms of appropriate representations for A, δ, F, f, m. These...
On the number of pairs of binary forms with given degree and given resultant
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