The Asymptotic Stability of x(n+ k) + ax(n) + bx(n− l) = 0

Abstract We established necessary and sufficient conditions for the asymptotic stability of the difference equation

x (n + k) + ax (n) + bx (n − l) = 0 , n = 0, 1, 2, ...,

where the coefficients a and b are real numbers and k and l are nonnegative integers.