Recurrent Sequences and Affine Functional Equations Original Research Article

Sárközy and other authors have characterized the multiplicative and the additive sequences among the solutionsg:image→image 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, Nset membership, variantimage with some coefficientsaset membership, variantimage,a*, q*set membership, variantimage,q*≠0. The results and methods of proof given in the present paper are new.