A pair of Goldbach-Linnik equations in unlike powers of primes and powers of two

TL;DR

This paper demonstrates that large even integers meeting specific conditions can be represented using a combination of primes, prime powers, and powers of two, extending the understanding of Goldbach-Linnik type equations.

Contribution

It introduces a new representation for large even integers involving primes, prime powers, and powers of two, under certain conditions.

Findings

Every large even integer satisfying certain conditions can be expressed as specified.

The representation involves primes, prime squares, prime cubes, and powers of two.

The result extends Goldbach-Linnik type equations to more complex compositions.

Abstract

In this paper, we show that every pair of large even integers satisfying certain necessary conditions can be expressed as a pair of one prime, one prime square, two prime cubes and 56 powers of 2.