@article{Huang2024, 
author = {Jing Huang and Qian Wang and Rui Zhang},
title = {On a binary Diophantine inequality involving prime numbers},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {4},
pages = {8371-8385},
keywords = {Diophantine inequality, prime, exponential sum},
url = {https://www.sciopen.com/article/10.3934/math.2024407},
doi = {10.3934/math.2024407},
abstract = {Let    N denote a sufficiently large real number. In this paper, we prove that for    1  <  c  <      104349    77419  ,    c  ≠      4    3  , for almost all real numbers    T  ∈  (  N  ,  2  N  ] (in the sense of Lebesgue measure), the Diophantine inequality        |        p    1    c    +      p    2    c    −  T      |    <      T          −              9                  10          c                            (                              104349            77419                    −          c                )             is solvable in primes        p    1    ,      p    2  . In addition, it is proved that the Diophantine inequality        |        p    1    c    +      p    2    c    +      p    3    c    +      p    4    c    −  N      |    <      N          −              9                  10          c                            (                              104349            77419                    −          c                )             is solvable in primes        p    1    ,      p    2    ,      p    3    ,      p    4  . This result constitutes a refinement upon that of Li and Cai.}
}