On a diophantine inequality with prime numbers of a special type

2017/01/26 by Tolev, D. I.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1701.07652

Abstract

We consider the Diophantine inequality | p₁^c + p₂^c + p₃^c- N | lt; (log N)^-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, p₃ + 2 has at most [ (369)/(180 - 168 c) ] prime factors, counted with the multiplicity.

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