Article ID: MTJPAM-D-21-00032

Title: On combinatorial formulation of Fermat quotients and generalization

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-21-00032; Volume 4 / Issue 1 / Year 2022, Pages 59-76

Document Type: Research Paper

Author(s): Mouloud Goubi a

aDepartment of Mathematics, University of UMMTO Tizi-Ouzou 15000, Algeria Algebra and Number Theory Laboratory, USTHB, Algiers

Received: 16 May 2021, Accepted: 7 October 2021, Published: 7 November 2021.

Corresponding Author: Mouloud Goubi (Email address:

Full Text: PDF


In this work we revisit the Fermat quotients to give their combinatorial formulae and study the corresponding vanishing congruences. The obtained results are used to resolve some problems encountered in the literature. To do this, we use the generating functions and Bell polynomials. In the final section, we introduce the convolved Fermat quotients and we give its recursive and combinatorial formulae.

Keywords: Fermat quotients, Fermat functions, congruences, p-adic numbers, Bell numbers, Bell polynomials

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