On pairs of one prime, four prime cubes and powers of 2

TL;DR

This paper proves that sufficiently large odd integer pairs can be simultaneously expressed using one prime, four prime cubes, and 231 powers of 2, advancing understanding of their additive representations.

Contribution

It introduces a new representation theorem for large odd integer pairs involving primes, prime cubes, and powers of 2, expanding additive number theory.

Findings

Every large odd integer pair can be represented as specified.

The representation involves only one prime, four prime cubes, and 231 powers of 2.

The result applies to sufficiently large integers, confirming a specific additive structure.

Abstract

In this paper, we consider the simultaneous representation of pairs of sufficiently large integers. We prove that every pair of large positive odd integers can be represented in the form of a pair of one prime, four cubes of primes and 231 powers of 2.