Integral Difference Ratio Functions on Integers

  • Patrick Cégielski
  • Serge Grigorieff
  • Irène GuessarianEmail author
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8808)


Various problems lead to the same class of functions from integers to integers: functions having integral difference ratio, i.e. verifying \(f(a)-f(b)\equiv 0 \pmod { (a-b)}\) for all \(a>b\). In this paper we characterize this class of functions from \({\mathbb Z}\) to \({\mathbb Z}\) 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.


Number Theory Theoretical Computer Science 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Patrick Cégielski
    • 1
  • Serge Grigorieff
    • 2
  • Irène Guessarian
    • 2
    Email author
  1. 1.LACL, EA 4219Université Paris-Est CréteilFontainebleauFrance
  2. 2.LIAFA, CNRS UMR 7089Université Paris 7 Denis DiderotParisFrance

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