On some Generalizations of Wilson's Theorem and How to Characterize Carmichael Numbers by Stirling Numbers

Khaled Ben Letaïef (1)

1 ISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'Espace

This work uses a combinatorial identity involving Stirling's numbers of the second kind to prove and generalize Wilson's theorem in an original manner. Then, again using this relation , we show new characterizations of Carmichael's numbers.

Mots clés: Stirling Numbers; Carmichael Numbers; Wilson's Theorem AMS Classification : 11B73; 05A18

Domaines: Mathématiques [math]; Combinatoire [math.CO]; Théorie des nombres [math.NT]

Khaled Ben Letaïef. On some Generalizations of Wilson's Theorem and How to Characterize Carmichael Numbers by Stirling Numbers. 2017. ⟨hal-01562678⟩