On a Diophantine equation with four prime variables
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.
Authors
- Jing-Song Huang (ORCID: https://orcid.org/0000-0001-6910-0606)
- Deyu Zhang (ORCID: https://orcid.org/0000-0002-6806-9528)
- Wenguang Zhai
Institutions
- China University of Mining and Technology (CN)
- Shandong Normal University (CN)
Publication Details
- Journal
- AIMS Mathematics
- Published
- 2025-01-01
- DOI
- https://doi.org/10.3934/math.2025652
- Primary Topic
- Analytic Number Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00