In the present paper, we first study Gaussian Leonardo numbers and hybrid numbers. We give some new results for numbers, including relations with Fibonacci Lucas also For proofs, use symmetric antisymmetric properties of Then, introduce polynomials, which can be considered as a generalization After that, using polynomials coefficients instead real in Moreover, obtain recurrence relations, gener...

Let $\lbrace U_n\rbrace =\lbrace U_n(P,Q)\rbrace $ and V_n\rbrace V_n(P,Q)\rbrace be the Lucas sequences of first second kind respectively at parameters $P \ge 1$ $Q \in \lbrace -1, 1\rbrace $. In this paper, we provide a technique for characterizing solutions 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 1$. Then, procedure is ...

Abstract We consider the Markoff–Rosenberger equation $$\begin{aligned} ax^2+by^2+cz^2=dxyz \end{aligned}$$ a x 2 + b y c z =</m...