Shnirelman's Theorem Applications

TL;DR

This paper explores applications of Shnirelman's theorem to Diophantine equations and investigates the representation of Gaussian integers as sums of odd Gaussian primes.

Contribution

It demonstrates new applications of Shnirelman's theorem to number theory problems involving Gaussian integers and primes.

Findings

Shnirelman's theorem can be effectively applied to Diophantine equations.

Representation of Gaussian integers by sums of odd Gaussian primes is feasible.

New insights into prime representations in Gaussian integers are provided.

Abstract

Shnirelman's theorem is applied to solving Diophantine equations, and also discussing of the problems of a representation of Gaussian integers by a sum of odd Gaussian primes.