Integral Difference Ratio Functions on Integers

Abstract : To Jozef, on his 80th birthday, with our gratitude for sharing with us his prophetic vision of Informatique Abstract. 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 a 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.
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Patrick Cégielski, Serge Grigorieff, Irene Guessarian. Integral Difference Ratio Functions on Integers. Computing with new resouces, 8808, pp.210-225, 2014, Lecture Notes in Computer Science, ⟨10.1007/978-3-319-13350-8_21⟩. ⟨hal-01259852⟩

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