Geodesic
Bartz-Marlewski equation with generalized Lucas components
Archivum mathematicum, Tome 58 (2022) no. 3, pp. 189-197

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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.
DOI : 10.5817/AM2022-3-189
Classification : 11B39, 11D45
Keywords: Lucas sequences; Diophantine equation 
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     author = {Hashim, Hayder R.},
     title = {Bartz-Marlewski equation with generalized {Lucas} components},
     journal = {Archivum mathematicum},
     pages = {189--197},
     publisher = {mathdoc},
     volume = {58},
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     doi = {10.5817/AM2022-3-189},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2022-3-189/}
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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

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