Functions with integer-valued divided differences.

Let s 0 , s 1 , s 2 , ... be a sequence of rational numbers whose m th divided difference δ m s is integer-valued. We prove that s n is a polynomial function in n if | s n | ≪ θ n for some positive number θ satisfying θ < e 1 + 1 2 + ⋯ + 1 m − 1. [ABSTRACT FROM AUTHOR]