On a Diophantine inequality with prime numbers of a special type

D. I. Tolev

Informatics and Automation, Analytic number theory, Tome 299 (2017), pp. 261-282.

Résumé

We consider the Diophantine inequality $|p_1^c+p_2^c+p_3^c-N|(\log N)^{-E}$, where $1$, $N$ is a sufficiently large real number and $E>0$ is an arbitrarily large constant. We prove that the above inequality has a solution in primes $p_1$, $p_2$, $p_3$ such that each of the numbers $p_1+2$, $p_2+2$ and $p_3+2$ has at most $[369/(180-168c)]$ prime factors, counted with multiplicity.

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