Work

On a Diophantine equation with four prime variables

Year: 2025

Type: article

Abstract: Let $ [\alpha] $ denote the integral part of the real number $ \alpha $, and let $ N $ be a sufficiently large integer. In this paper, we proved that for $ 1 < c < \frac{38}{29} $, almost all $ n\in(N, 2N] $ can be represented as $ [p_1^c]+[p_2^c]+[p_3^c]+[p_4^c] = n $, where $ p_1, p_2, p_3, p_4 $ are prime numbers.

Source: AIMS Mathematics

DOI: 10.3934/math.2025652

Authors: Jing Huang, Wenguang Zhai, Deyu Zhang

Institutions: Shandong Normal University, China University of Mining and Technology - Beijing

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funder: National Natural Science Foundation of China