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We study in this paper the following max-type system of difference equations of higher order: and , , where , , and the initial conditions . We show that if , then every solution of the above system is periodic with period eventually. If , then every solution of the above system is periodic with period or eventually. If or , then the above system has a solution which is not periodic eventually.

Eventually Periodic Solutions of a Max-Type System of Difference Equations of Higher Order