On a diophantine inequality with prime numbers of a special type

D. I. Tolev

We consider the Diophantine inequality \[ \left| p_1^{c} + p_2^{c} + p_3^c- N \right| < (\log N)^{-E} , \] where $1<c<\frac{15}{14}$, $N$ is a sufficiently large real number an…