Conditions for the Existence of Power Solutions to a Linear Difference Equation with Constant Coefficients

With the help of the formula for the general solution of a difference equation with constant coefficients, it is shown that the set of solutions to this equation contains classical solutions of the type \({{k}^{m}}{{\lambda }^{k}}\) . We present necessary and sufficient conditions on the coefficients of the equation and the initial parameters under which such solutions are obtained.