Some interesting number theory problems

TL;DR

This paper introduces intriguing number theory problems involving Legendre's symbol and two-term exponential sums, aiming to stimulate further research in these mathematical areas.

Contribution

It proposes new, interesting problems in number theory related to Legendre's symbol and exponential sums, expanding the scope of current research.

Findings

Proposed novel problems in number theory.

Highlighted connections between Legendre's symbol and exponential sums.

Encouraged future exploration of these problems.

Abstract

The main purpose of this paper is to propose some interesting number theory problems related to the Legendre's symbol and the two-term exponential sums.