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Baker's explicit abc-conjecture and applications

Shanta Laishram, T. N. Shorey (2012)

Acta Arithmetica

Bartz-Marlewski equation with generalized Lucas components

Hayder R. Hashim (2022)

Archivum Mathematicum

Let ${U_{n}} = {U_{n} (P, Q)}$ and ${V_{n}} = {V_{n} (P, Q)}$ be the Lucas sequences of the first and second kind respectively at the parameters $P \geq 1$ and $Q \in {- 1, 1}$ . In this paper, we provide a technique for characterizing the solutions of the so-called Bartz-Marlewski equation $x^{2} - 3 x y + y^{2} + x = 0,$ where $(x, y) = (U_{i}, U_{j})$ or $(V_{i}, V_{j})$ with $i$ , $j \geq 1$ . Then, the procedure of this technique is applied to completely resolve this equation with certain values of such parameters.

Basic bounds of Fréchet classes

Jaroslav Skřivánek (2014)

Kybernetika

Algebraic bounds of Fréchet classes of copulas can be derived from the fundamental attributes of the associated copulas. A minimal system of algebraic bounds and related basic bounds can be defined using properties of pointed convex polyhedral cones and their relationship with non-negative solutions of systems of linear homogeneous Diophantine equations, largely studied in Combinatorics. The basic bounds are an algebraic improving of the Fréchet-Hoeffding bounds. We provide conditions of compatibility...

Bemerkung zu der Abhandlung des Herrn P.v. Schaewen, Jahresbericht Bd. 18, S. 7 ff.

Julius v. S v. Nagy (1909)

Jahresbericht der Deutschen Mathematiker-Vereinigung

Berichtigung zu "Über die Darstellung der Primzahlen der Form 4n + 1 als Summe zweier Quadrate".

Ernst Jacobsthal (1907)

Journal für die reine und angewandte Mathematik

Bernoulli numbers, Hurwitz numbers, p-adic L-functions and Kummer's criterion.

Alvaro Lozano Robledo (2007)

RACSAM

Let K = Q(ζp) and let hp be its class number. Kummer showed that p divides hp if and only if p divides the numerator of some Bernoulli number. In this expository note we discuss the generalizations of this type of criterion to totally real fields and quadratic imaginary fields.

Bihomogeneous forms in many variables

Damaris Schindler (2014)

Journal de Théorie des Nombres de Bordeaux

We count integer points on varieties given by bihomogeneous equations using the Hardy-Littlewood method. The main novelty lies in using the structure of bihomogeneous equations to obtain asymptotics in generically fewer variables than would be necessary in using the standard approach for homogeneous varieties. Also, we consider counting functions where not all the variables have to lie in intervals of the same size, which arises as a natural question in the setting of bihomogeneous varieties.