# On a system of difference equations of third order solved in closed form

## Main Article Content

## Abstract

x

_{n+1}=(ay

_{n-2}x

_{n-1}y

_{n}+bx

_{n-1}y

_{n}

_{-2}+cy

_{n}

_{-2}+d)/(y

_{n-2}x

_{n-1}y

_{n}),

y

_{n+1}=(ax

_{n-2}y

_{n-1}x

_{n}+by

_{n-1}x

_{n}

_{-2}+cx

_{n}

_{-2}+d)/(x

_{n-2}y

_{n-1}x

_{n}),

where n belongs to the set of positive integer numbers, x

_{-2}, x

_{-1}, x

_{0}, y

_{-2}, y

_{-1}and y

_{0}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.

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.

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## Article Details

*Journal of Innovative Applied Mathematics and Computational Sciences*. 1, 1 (Dec. 2021), 1–15. DOI:https://doi.org/10.58205/jiamcs.v1i1.8.

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