A quaternary diophantine inequality by prime numbers of a special type

S. I. Dimitrov

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 sol…