Binary Additive Problems: Theorems of Landau and Hardy-Littlwood Type

TL;DR

This paper proves theorems related to binary additive problems, such as Goldbach and Chen conjectures, using uniform positions, and introduces new conjectures in the field.

Contribution

It establishes new theorems of Landau and Hardy-Littlewood type for various binary partitions and proposes novel conjectures.

Findings

Proved theorems for Goldbach and Chen problems

Extended results to Lemoine-Levy and other binary partitions

Posed new conjectures in binary additive number theory

Abstract

With the uniform positions we prove theorems of Landau and Hardy-Littlwood type for Goldbach, Chen, Lemoine-Levy and other binary partitions of positive integers. We also pose some new conjectures.