On the Newman sum over multiples of a prime with a primitive or semiprimitive root 2

TL;DR

This paper derives simple relations for the Newman sum over multiples of primes with primitive or semiprimitive root 2, including the specific case of p=17, contributing to the understanding of these sums in number theory.

Contribution

It introduces new simple relations for Newman sums over certain primes with specific roots, expanding the theoretical framework in number theory.

Findings

Derived relations for Newman sums over primes with primitive or semiprimitive root 2

Analyzed the case of p=17 in detail

Enhanced understanding of Newman sums in number theory

Abstract

We obtain a simple relations for the Newman sum over multiples of a prime with a primitive or semiprimitive root 2. We consider the case of p=17 as well.