On NP complete problems I

TL;DR

This paper investigates the NP-complete quadratic residue problem, arguing that due to the random distribution of solutions, it cannot be solved by nondeterministic polynomial processes, implying it does not belong to class P.

Contribution

It provides a novel analysis linking prime numbers and solution distribution to the complexity class of the quadratic residue problem.

Findings

Quadratic residue problem is NP-complete.

Solution distribution appears random.

Nondeterministic polynomial processes are insufficient.

Abstract

We study the quadratic residue problem known as an NP complete problem by way of the prime number and show that a nondeterministic polynomial process does not belong to the class P because of a random distribution of solutions for the quadratic residue problem.