Titre : A new generalization of the Genocchi numbers and its consequence on the Bernoulli polynomials Auteurs : Bakir Farhi, Revue : Advances in Pure and Applied Mathematics Numéro : Issue 4 (September 2022) Volume : 13 Date : 2022/10/21 DOI : 10.21494/ISTE.OP.2022.0886 ISSN : 1869-6090 Résumé : This paper presents a new generalization of the Genocchi numbers and the Genocchi theorem. As consequences, we obtain some important families of integer-valued polynomials those are closely related to the Bernoulli polynomials. Denoting by $$${(B_n)}_{n \in \mathbb{N}}$$$ the sequence of the Bernoulli numbers and by $$${(B_n(X))}_{n \in \mathbb{N}}$$$ the sequence of the Bernoulli polynomials, we especially obtain that for any natural number $$$n$$$, the reciprocal polynomial of the polynomial $$$\big(B_n(X) - B_n\big)$$$ is integer-valued. Éditeur : ISTE OpenScience