MMN-2498
Identities and congruences involving the geometric polynomials
Miloud Mihoubi; Said Taharbouchet;Abstract
In this paper, we investigate the umbral
representation of the Fubini polynomials $\mathbf{F}_{\mathbf{x}}^{n}:=%
\mathcal{F}_{n} ( x ) $ to derive some properties involving these
polynomials. Furthermore, for any prime number $p$ and any polynomial $f$ with integer
coefficients, we show $ ( f ( \mathbf{F}_{\mathbf{x}} ) )
^{p}\equiv f ( \mathbf{F}_{\mathbf{x}} ) $ (mod $p$) and we give other
curious congruences.
Vol. 20 (2019), No. 1, pp. 395-408
DOI: 10.18514/MMN.2019.2498