Wolstenholme primes and group determinants of cyclic groups

Abstract

A Wolstenholme prime is a prime number $p \geq 5$ that divides the numerator of the Bernoulli number $B_{p-3}$. A number of equivalent definitions for Wolstenholme primes are known, mainly related to congruences of harmonic sums or binomial coefficients. In this paper, we introduce an equivalent definition of Wolstelholme primes related to the number of terms in the group determinant of cyclic groups, and equivalently, the cardinality of certain sets of restricted partitions.