On a Diophantine Inequality with Prime Numbers of a Special Type

Аннотация

We consider the Diophantine inequality |p₁^c + p₂^c + p₃^c − N| < (logN)^−E, where 1 < c < 15/14, 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 p₁, p₂, p₃ such that each of the numbers p₁ + 2, p₂ + 2 and p₃ + 2 has at most [369/(180 − 168c)] prime factors, counted with multiplicity.