On The Solutions of Three-Dimensional Difference Equation Systems Via Pell Numbers

Year 2022, Issue: 34, 433 - 440, 31.03.2022

Necati Taşkara Hüseyin Büyük

https://doi.org/10.31590/ejosat.1082643

Abstract

In this study, we investigate the form of the solutions of the following rational difference equation system
x_n=(z_(n-1) z_(n-3))/(x_(n-2)+2z_(n-3) ),y_n=(x_(n-1) x_(n-3))/(〖-y〗_(n-2)+6x_(n-3) ),z_n=(y_(n-1) y_(n-3))/(z_(n-2)+14y_(n-3) ) ,n∈N_0
where initial values〖 x〗_(-3) 〖,x〗_(-2), x_(-1),y_(-3),y_(-2),y_(-1),〖 z〗_(-3),〖 z〗_(-2),〖 z〗_(-1) are nonzero real numbers, such that their solutions are associated with Pell numbers. We also give a relationships between Pell numbers and solutions of systems

Keywords

System of difference equations, Pell numbers, Representation of solutions, Binet formula, Solutions

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