General solutions to systems of difference equations and some of their representations. (English) Zbl 1490.39012
Summary: Here we solve the following system of difference equations
\[x^{(j)}_{n+1}=\frac{F_{m+2}+F_{m+1}x^{((j+1)\bmod(p))}_{n-k}}{F_{m+3} +F_{m+2}x^{((j+1)\bmod(p))}_{n-k}},\quad n,m, p, k \in N_0, j=\overline{1,p},\]
where \((F_n)_{n=0}^{+\infty}\) is the Fibonacci sequence. We give a representation of its general solution in terms of Fibonacci numbers and the initial values. Some theoretical justifications related to the representation for the general solution are also given.
MSC:
| 39A20 | Multiplicative and other generalized difference equations |
| 11B39 | Fibonacci and Lucas numbers and polynomials and generalizations |
| 11B83 | Special sequences and polynomials |
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