Two‐dimensional solvable system of difference equations with periodic coefficients

We show that the following two‐dimensional system of difference equations:x n + 1 =a nx n+b ny n,y n + 1 =c nx n+d ny n, n ∈ N 0 , where( a n ) n ∈ N 0,( b n ) n ∈ N 0,( c n ) n ∈ N 0, and( d n ) n ∈ N 0are periodic sequences, is solvable, considerably extending some results in the literature. In the case when all these four sequences are periodic with period 2 or with period 3, we present closed‐form formulas for the general solutions to the corresponding systems of difference equations. Some comments regarding theoretical and practical solvability of the system, connected to the value of the period of the sequences, are given.