Abstract
We consider the Diophantine inequality |p c1 + p c2 + p c3 − 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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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Vol. 299, pp. 261–282.
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Tolev, D.I. On a Diophantine Inequality with Prime Numbers of a Special Type. Proc. Steklov Inst. Math. 299, 246–267 (2017). https://doi.org/10.1134/S0081543817080168
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DOI: https://doi.org/10.1134/S0081543817080168