@ARTICLE{10.21494/ISTE.OP.2022.0886, 

TITLE={Une nouvelle géneralisation des nombres de Genocchi et  conséquence sur les polynômes de Bernoulli}, 
  
AUTHOR={Bakir Farhi, }, 
	
JOURNAL={Avancées en Mathématiques Pures et Appliquées}, 
	
VOLUME={13}, 

NUMBER={Numéro 4 (Septembre 2022)}, 
	
YEAR={2022}, 

URL={https://www.openscience.fr/Une-nouvelle-generalisation-des-nombres-de-Genocchi-et-consequence-sur-les}, 
	
DOI={10.21494/ISTE.OP.2022.0886}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={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.}}