Identities and congruences involving the Fubini polynomials

Miloud Mihoubi; Said Taharbouchet

Identities and congruences involving the Fubini polynomials

Number Theory 2017-06-28 v1

Authors: Miloud Mihoubi , Said Taharbouchet

Abstract

In this paper, we investigate the umbral representation of the Fubini polynomials $F_{x}^{n}:=F_{n}(x)$ to derive some properties involving these polynomials. For any prime number $p$ and any polynomial $f$ with integer coefficients, we show $(f(F_{x}))^{p}\equiv f(F_{x})$ and we give other curious congruences.

Keywords

Fubini polynomials umbral representation congruences identities prime numbers integer coefficients

Cite

@article{arxiv.1706.08950,
  title  = {Identities and congruences involving the Fubini polynomials},
  author = {Miloud Mihoubi and Said Taharbouchet},
  journal= {arXiv preprint arXiv:1706.08950},
  year   = {2017}
}

Comments

12 pages

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