A quaternary diophantine inequality by prime numbers of a special type

Abstract

Let $1<c<832/825$. For large real numbers $N>0$ and a small constant $\vartheta >0$, the inequality \begin{equation*} |p_1^c+p_2^c+p_3^c+p_4^c-N|<\vartheta \end{equation*} has a solution in prime numbers $p_1,p_2,p_3,p_4$ such that, for each $i\in \{1,2,3,4\}$, $p_i+2$ has at most $32$ prime factors.

References in corpus (1)

• On a diophantine inequality with prime numbers of a special type