Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Waring-Goldbach problems for one square and higher powers

Geovane Matheus Lemes Andrade

Abstract

We prove that every sufficiently large odd integer can be expressed as a sum of one square and fourteen fifth powers, all of primes. In addition, we establish that every sufficiently large even integer can be written as a sum of one square, one biquadrate, and twelve fifth powers of primes.

Waring-Goldbach problems for one square and higher powers

Abstract

We prove that every sufficiently large odd integer can be expressed as a sum of one square and fourteen fifth powers, all of primes. In addition, we establish that every sufficiently large even integer can be written as a sum of one square, one biquadrate, and twelve fifth powers of primes.
Paper Structure (4 sections, 6 theorems, 55 equations)

This paper contains 4 sections, 6 theorems, 55 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The major arcs
  4. The minor arcs

Key Result

Theorem 1

For each sufficiently large odd integer $n$, the equation admits a solution in which all variables are prime. Moreover, for every sufficiently large even integer $n$, the equation has a solution with all $x_j$ prime.

Theorems & Definitions (9)

  • Theorem 1
  • Lemma 2
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Lemma 5
  • proof
  • Lemma 6