Integral Difference Ratio Functions on Integers
نویسندگان
چکیده
Various problems lead to the same class of functions from integers to integers: functions having integral difference ratio, i.e. verifying f(a) − f(b) ≡ 0 (mod (a − b)) for all a > b. In this paper we characterize this class of functions from Z to Z via their à la Newton series expansions on a suitably chosen basis of polynomials (with rational coefficients). We also exhibit an example of such a function which is not polynomial but Bessel like.
منابع مشابه
Newton representation of functions over natural integers having integral difference ratios
Different questions lead to the same class of functions from natural integers to integers: those which have integral difference ratios, i.e. verifying f(a)− f(b) ≡ 0 (mod (a− b)) for all a > b. We characterize this class of functions via their representations as Newton series. This class, which obviously contains all polynomials with integral coefficients, also contains unexpected functions, fo...
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تاریخ انتشار 2014