Two Digit Theorems

TL;DR

This paper investigates properties of prime numbers with primitive roots, establishing specific equalities involving exponential sums and providing conditions for similar equalities to hold.

Contribution

It proves that primes with primitive root 2 satisfy a particular exponential sum equality and offers a sufficient condition for related equalities.

Findings

Primes with primitive root 2 satisfy S_p(2^p)=p.

Provides a sufficient condition for S_p(2^p)=±p.

Advances understanding of exponential sums related to primitive roots.

Abstract

We prove that if p is a prime with a primitive root 2 then S_p(2^p)=p and give a sufficient condition for an equality of kind S_p(2^p)=+or-p.