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Integral Difference Ratio Functions on Integers

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8808)

Abstract

Various problems lead to the same class of functions from integers to integers: functions having integral difference ratio, i.e. verifying \(f(a)-f(b)\equiv 0 \pmod { (a-b)}\) 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.

Keywords

  • Number Theory
  • Theoretical Computer Science

Partially supported by TARMAC ANR agreement 12 BS02 007 01.

Irène Guessarian: Emeritus at UPMC Université Paris 6.

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Correspondence to Irène Guessarian .

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Cégielski, P., Grigorieff, S., Guessarian, I. (2014). Integral Difference Ratio Functions on Integers. In: Calude, C., Freivalds, R., Kazuo, I. (eds) Computing with New Resources. Lecture Notes in Computer Science(), vol 8808. Springer, Cham. https://doi.org/10.1007/978-3-319-13350-8_21

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  • DOI: https://doi.org/10.1007/978-3-319-13350-8_21

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  • Publisher Name: Springer, Cham

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