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.
Partially supported by TARMAC ANR agreement 12 BS02 007 01.
Irène Guessarian: Emeritus at UPMC Université Paris 6.
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© 2014 Springer International Publishing Switzerland
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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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