Periodic Solutions to a Third-Order Conditional Difference Equation over the Integers

الملخص EN

This paper studies a third-order conditional difference equation which is a generalization from the literature.

We investigate this equation by transforming it into a first-order system.

Finally it is proved that the equation has no period-two (or three) integer solutions.

Besides, its all period-four (and five) integer solutions are derived under appropriate rational parameters.