Congruence properties of prime sums and Bernoulli polynomials

TL;DR

This paper explores congruence properties of sums involving prime numbers and Bernoulli polynomials, deriving new relations that connect prime sums with Bernoulli numbers in modular arithmetic.

Contribution

It introduces novel congruence relations linking prime sums and Bernoulli polynomials, expanding understanding of their algebraic properties.

Findings

Derived a new congruence property involving prime sums and Bernoulli numbers.

Established a general congruence relation for Bernoulli polynomials.

Connected prime sum rules with Bernoulli polynomial congruences.

Abstract

In this article, we derive a congruence property of particular sum rules involving prime numbers. The resulting expression involves Bernoulli numbers and polynomials, for which we obtain, as a consequence, a general congruence relation as well.