Etude probabiliste des p-quotients de Fermat

Georges Gras (1)

1 Chercheur indépendant

For a fixed integer a>1, we suggest that the probability of nullity of the p-Fermat quotient q(p,a) is much lower than 1/p for any arbitrary large prime number p. For this we use various heuristics, justified by means of numerical computations and analytical results, which may imply the finiteness of the q(p,a) equal to 0 and the existence of integers a such that q(p,a) is different from 0 for all p. However no proofs are obtained concerning these heuristics.

Mots clés: Fermat quotients; cyclotomic polynomials; probabilistic number theory

Domaines: Théorie des nombres [math.NT]

Georges Gras. Etude probabiliste des p-quotients de Fermat. 2014. ⟨hal-01062305v1⟩