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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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Dates and versions

hal-01259852 , version 1 (25-01-2016)

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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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