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

TL;DR

This paper proves that large odd integers can be expressed as a sum involving one prime, four prime cubes, and 48 powers of 2, advancing understanding of additive number theory problems.

Contribution

It establishes a new representation theorem for large odd integers involving primes, prime cubes, and powers of 2, extending classical Goldbach-Linnik problems.

Findings

Every sufficiently large odd integer can be represented as specified.

The representation involves one prime, four prime cubes, and 48 powers of 2.

The result generalizes previous additive number theory results.

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 $2$.