Address: Faculty of Computer Science and Mathematics, University of Kufa, P.O.Box 21, 54001 Al Najaf, Iraq
E-mail: hayderr.almuswi@uokufa.edu.iq
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.
AMSclassification: primary 11D45; secondary 11B39.
Keywords: Lucas sequences, Diophantine equation.
DOI: 10.5817/AM2022-3-189