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Goldbach-Linnik type problems involving one prime, four prime cubes and powers of 2

Xue Han, Huafeng Liu

Abstract

In this paper, we prove that every pair of sufficiently large odd integers can be represented in the form of a pair of one prime, four prime cubes and $48$ powers of $2$.

Goldbach-Linnik type problems involving one prime, four prime cubes and powers of 2

Abstract

In this paper, we prove that every pair of sufficiently large odd integers can be represented in the form of a pair of one prime, four prime cubes and powers of .
Paper Structure (4 sections, 12 theorems, 88 equations)

This paper contains 4 sections, 12 theorems, 88 equations.

Table of Contents

  1. Introduction
  2. Outline of the proof
  3. Auxiliary lemmas
  4. Proof of Theorem \ref{['thm1']}

Key Result

Theorem 1

The equations main with $k=48$ are solvable for every pair of sufficiently large odd integers $N_{1}$ and $N_{2}$ with $N_{1} \asymp N_{2}$.

Theorems & Definitions (23)

  • Theorem 1
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • Lemma 3.4
  • proof
  • Lemma 3.5
  • ...and 13 more