Voronoï type congruences and its applications

Takashi Agoh

Abstract

In this paper, we will first deduce Voronoï  type congruences for Bernoulli numbers in the even suffix notation. Continuously, we will apply them to extend very important arithmetic properties (such as von Staudt-Clausen's and Kummer's congruences) of these numbers to more general situation.

Keywords

Bernoulli numbers, von Staudt-Clausen's theorem, Voronoï's congruence, Kummer's congruence, irregular primes

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