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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.

Barycentric Ramsey numbers for small graphs.

González, Samuel, González, Leida, Ordaz, Oscar (2009)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Barycentric-sum problems: a survey.

Ordaz, Oscar, Quiroz, Domingo (2007)

Divulgaciones Matemáticas

Beatty sequences and multiplicative number theory

Abercrombie Alex G. (1995)

Acta Arithmetica

Behrend-type constructions for sets of linear equations

Asaf Shapira (2006)

Acta Arithmetica

Beiträge zu der Kenntniss der Bernouillischen Zahlen.

R. Lipschitz (1884)

Journal für die reine und angewandte Mathematik

Beleuchtung und Beweis eines Satzes aus Legendre's Zahlentheorie [Book]

Hermann Scheffler (1893)

Bell and Stirling numbers for graphs.

Duncan, Bryce, Peele, Rhodes (2009)

Journal of Integer Sequences [electronic only]

Bell polynomials and degenerate stirling numbers

F. T. Howard (1979)

Rendiconti del Seminario Matematico della Università di Padova

Bemerkung zu einer Anwendung des Bertrandschen Postulats in der Zahlentheorie.

Tibor Salát (1971)

Elemente der Mathematik

Bender's generalized q-binominal Vandermonde convolution.

Ronald J. Evans (1978)

Aequationes mathematicae

Benford's law, values of L-functions and the 3x+1 problem

Alex V. Kontorovich, Steven J. Miller (2005)

Acta Arithmetica

Berechnung der Werte von Zetafunktionen totalreeller kubischer Zahlkörper an ganzzahligen Stellen mittels verallgemeinerter Dedekindscher Summen. I.

Ulrich Halbritter (1985)

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.

Bernoulli-Dedekind sums

Matthias Beck, Anastasia Chavez (2011)

Acta Arithmetica

Best simultaneous diophantine approximations of some cubic algebraic numbers

Nicolas Chevallier (2002)

Journal de théorie des nombres de Bordeaux

Let $α$ be a real algebraic number of degree $3$ over $ℚ$ whose conjugates are not real. There exists an unit $ζ$ of the ring of integer of $K = ℚ (α)$ for which it is possible to describe the set of all best approximation vectors of $θ = (ζ, ζ^{2})$ .’

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