Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On sums of unequal powers of primes and powers of 2

Yuhui Liu

Abstract

In this paper, it is proved that every sufficiently large even integer can be represented as the sum of two squares of primes, two cubes of primes, two biquadrates of primes and 16 powers of 2. Furthermore, there are at least 5.313% odd integers that can be represented as one square of prime, one cube of prime and one biquadrate of prime. This result constitutes a refinement upon that of R. Zhang [8].

On sums of unequal powers of primes and powers of 2

Abstract

In this paper, it is proved that every sufficiently large even integer can be represented as the sum of two squares of primes, two cubes of primes, two biquadrates of primes and 16 powers of 2. Furthermore, there are at least 5.313% odd integers that can be represented as one square of prime, one cube of prime and one biquadrate of prime. This result constitutes a refinement upon that of R. Zhang [8].
Paper Structure (5 sections, 53 equations)

This paper contains 5 sections, 53 equations.

Table of Contents

  1. Introduction
  2. Notation and Some Preliminary Lemmas
  3. Auxiliary Estimates
  4. Proof of Theorem 1.1
  5. Proof of Theorem 1.2