Bartz-Marlewski equation with generalized Lucas components
Archivum Mathematicum (2022)
- Volume: 058, Issue: 3, page 189-197
- ISSN: 0044-8753
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topHashim, Hayder R.. "Bartz-Marlewski equation with generalized Lucas components." Archivum Mathematicum 058.3 (2022): 189-197. <http://eudml.org/doc/298461>.
@article{Hashim2022,
abstract = {Let $\lbrace U_n\rbrace =\lbrace U_n(P,Q)\rbrace $ and $\lbrace V_n\rbrace =\lbrace V_n(P,Q)\rbrace $ be the Lucas sequences of the first and second kind respectively at the parameters $P \ge 1$ and $Q \in \lbrace -1, 1\rbrace $. 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 $(x,y)=(U_i, U_j)$ or $(V_i, V_j)$ with $i$, $ j \ge 1$. Then, the procedure of this technique is applied to completely resolve this equation with certain values of such parameters.},
author = {Hashim, Hayder R.},
journal = {Archivum Mathematicum},
keywords = {Lucas sequences; Diophantine equation},
language = {eng},
number = {3},
pages = {189-197},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Bartz-Marlewski equation with generalized Lucas components},
url = {http://eudml.org/doc/298461},
volume = {058},
year = {2022},
}
TY - JOUR
AU - Hashim, Hayder R.
TI - Bartz-Marlewski equation with generalized Lucas components
JO - Archivum Mathematicum
PY - 2022
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 058
IS - 3
SP - 189
EP - 197
AB - Let $\lbrace U_n\rbrace =\lbrace U_n(P,Q)\rbrace $ and $\lbrace V_n\rbrace =\lbrace V_n(P,Q)\rbrace $ be the Lucas sequences of the first and second kind respectively at the parameters $P \ge 1$ and $Q \in \lbrace -1, 1\rbrace $. 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 $(x,y)=(U_i, U_j)$ or $(V_i, V_j)$ with $i$, $ j \ge 1$. Then, the procedure of this technique is applied to completely resolve this equation with certain values of such parameters.
LA - eng
KW - Lucas sequences; Diophantine equation
UR - http://eudml.org/doc/298461
ER -
References
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