TY - JOUR AU - AKROUR, Youssouf AU - Touafek, Nouressadat AU - Halim, Yacine PY - 2021/12/22 Y2 - 2024/03/29 TI - On a system of difference equations of third order solved in closed form JF - Journal of Innovative Applied Mathematics and Computational Sciences JA - J. Innov. Appl. Math. Comput. Sci VL - 1 IS - 1 SE - Research Articles DO - 10.58205/jiamcs.v1i1.8 UR - https://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/v1i1-08 SP - 1-15 AB - <pre>In this work, we show that the system of difference equations<br />x<sub>n+1</sub>=(ay<sub>n-2</sub>x<sub>n-1</sub>y<sub>n</sub>+bx<sub>n-1</sub>y<sub>n</sub><sub>-2</sub>+cy<sub>n</sub><sub>-2</sub>+d)/(y<sub>n-2</sub>x<sub>n-1</sub>y<sub>n</sub>),<br />y<sub>n+1</sub>=(ax<sub>n-2</sub>y<sub>n-1</sub>x<sub>n</sub>+by<sub>n-1</sub>x<sub>n</sub><sub>-2</sub>+cx<sub>n</sub><sub>-2</sub>+d)/(x<sub>n-2</sub>y<sub>n-1</sub>x<sub>n</sub>),<br />where n belongs to the set of positive integer numbers, x<sub>-2</sub>, x<sub>-1</sub>, x<sub>0</sub>, y<sub>-2</sub>, y<sub>-1</sub> and y<sub>0</sub> are arbitrary nonzero real numbers, and the parameters a, b, c and d are arbitrary real numbers with d nonzero can be solved in a closed form.<br />We will see that when a = b = c = d = 1, the solutions are expressed using the famous Tetranacci numbers. In particular, the results obtained here extend those in our recent work.</pre> ER -