The Landau's problems. I-II

TL;DR

This paper presents solutions to all four of Landau's famous problems in number theory, including a proof of Goldbach's conjecture, addressing longstanding mathematical questions from 1912.

Contribution

It provides the first proof of Goldbach's conjecture and solutions to the remaining three Landau's problems, advancing fundamental understanding in number theory.

Findings

Proof of Goldbach's conjecture established

Solutions to the other three Landau's problems provided

Significant progress in solving classical number theory problems

Abstract

This is a work in two parts devoted to solutions of the so-called {\em four Landau's problems} in Number Theory, listed by Edmund Landau at the 1912 International Congress of Mathematics. In Part I the {\em Goldbach's conjecture} is proved. (This is the first Landau's problems.) In Part II the other three Landau's problems are considered and solved too.