Proceedings of the Steklov Institute of Mathematics

, Volume 299, Issue 1, pp 246–267 | Cite as

On a Diophantine Inequality with Prime Numbers of a Special Type

  • D. I. Tolev


We consider the Diophantine inequality |p 1 c + p 2 c + p 3 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.


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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Faculty of Mathematics and InformaticsSofia University “St. Kliment Ohridski,”SofiaBulgaria

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