Factorization of numbers with Gauss sums: I. Mathematical background

TL;DR

This paper explores a mathematical approach to factor numbers using the periodicity of Gauss sums, providing rules and examples for a factorization method based on interference effects.

Contribution

It introduces a novel factorization scheme leveraging Gauss sums' properties, with detailed mathematical background and illustrative examples.

Findings

The method effectively factors numbers using interference patterns.

The algorithm relies solely on interference and scales exponentially.

Rules for identifying factors are systematically derived.

Abstract

We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and scales exponentially.