The Solutions of Systems of Rational Difference Equations in Terms of Fibonacci Numbers

Elsayed, Elsayed M.; Alharthi, Mai

The Solutions of Systems of Rational Difference Equations in Terms of Fibonacci Numbers

Document Type : Original Article

Authors

Elsayed M. Elsayed ¹^{, 2}
Mai Alharthi ¹^{, 3}

¹ Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia

² Department of Mathematics Faculty of Science, Mansoura University, Mansoura, 35516 , Egypt

³ Department of Mathematics, Faculty of Science, Jeddah University, Jeddah, Kingdom of Saudi Arabia.

Abstract

In this paper, we get the form of the solutions of the following difference equation systems with nonzero real numbers initial conditions

z(n+1) =w(n)(z(n-4) + w(n-5))/w(n-5) + z(n-4) - w(n),

w(n+1) =z(n-3)(z(n-3) + w(n-4)/2z(n-3) + w(n-4).

z(n+1) =w(n)(w(n-5) -z(n-4))/w(n-5)- z(n-4) + w(n),

w(n+1) =z(n-3)(w(n-4) -z(n-3)/w(n-4)

Keywords