Goldbach–Linnik type problems with one prime square and six prime cubes

School of Cybersecurity, Shandong University of Political Science and Law, Jinan 250014, Shandong, China

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 23 September 2025
Accepted: 3 April 2026

Abstract

Let p₁, p₂, …, p₇ be prime numbers. In this paper, we first show that when k₁ ≥ 49, any sufficiently large odd integer can be represented as the sum of a prime square, six prime cubes and k₁ powers of 2. Furthermore, we prove that for k₂ ≥ 73, every pair of sufficiently large odd integers can be expressed as a pair of equations involving a prime square, six prime cubes and k₂ powers of 2.