Recurrent Sequences and Affine Functional Equations

AbstractSárközy and other authors have characterized the multiplicative and the additive sequences among the solutionsg:N→C of homogeneous linear recurrence equations with complex coefficients. Their results are special cases of a much more general theorem concerning recurrent sequencesgsatisfying certain functional equations of the typeg(nq+a)=q*g(n)+a* (n=1, …, N) for sufficiently largeq, N∈N with some coefficientsa∈N,a*, q*∈C,q*≠0. The results and methods of proof given in the present paper are new