In this study, we investigate the form of the solutions of the following rational difference equation systems 1 1 1      such that their solutions are associated with Padovan numbers.

In this study, we investigate the solutions of two special types of the Riccati difference equation x n+1 = 1 1+x n and y n+1 = 1 -1+y n such that their solutions are associated with Fibonacci numbers.

An analysis of semi‐cycles of positive solutions to eight systems of difference equations of the following form xn=a+pn−1qn−2pn−1+qn−2,yn=a+rn−1sn−2rn−1+sn−2,n∈double-struckN0, where a ∈ [0, + ∞), the sequences pn, qn, rn, sn are some of the sequences xn and yn, with positive initial values x−j,y−j, j = 1,2, is conducted in detail, and it is shown that these systems can be solved in closed‐form, which is the main result here. Two methods for showing the solvability are described.

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We have studied recently solvability and semi‐cycles of eight systems of difference equations of the following form: xn=a+pn−1qn−2pn−1+qn−2,yn=a+rn−1sn−2rn−1+sn−2,n∈double-struckN0, where a ∈ [0, + ∞), the sequences pn, qn, rn, sn are some of the sequences xn and yn, with positive initial values x−j,y−j, j = 1,2, in detail. This paper is devoted to the study of the other eight systems of the form. We show that these systems are also solvable in closed form and describe semi‐cycles of their solutions complementing our previous results on such systems of difference equations.