Bartz-Marlewski equation with generalized Lucas components

Hashim, Hayder R.

doi:10.5817/AM2022-3-189

Geodesic

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Bartz-Marlewski equation with generalized Lucas components

Hashim, Hayder R.

Archivum mathematicum, Tome 58 (2022) no. 3, pp. 189-197.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Résumé

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 \[ x^2-3xy+y^2+x=0\,, \] where

(x, y) = (U_{i}, U_{j})

(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.

MR Zbl

DOI : 10.5817/AM2022-3-189

Classification : 11B39, 11D45
Mots-clés : Lucas sequences; Diophantine equation

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     title = {Bartz-Marlewski equation with generalized {Lucas} components},
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Hashim, Hayder R. Bartz-Marlewski equation with generalized Lucas components. Archivum mathematicum, Tome 58 (2022) no. 3, pp. 189-197. doi : 10.5817/AM2022-3-189. https://geodesic-test.mathdoc.fr/articles/10.5817/AM2022-3-189/

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