A ternary diophantine inequality with prime numbers of a special type
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We consider the inequality $$|p^{c}_{1}+ p^{c}_{2}+ p^{c}_{3}− N| < (log N)^{−E},$$ where $1$ < $c$ < $\frac{281}{250}$ , $N$ 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 $p_{1} + 2, p_{2} + 2, p_{3} + 2$ has at most [$\frac{1475}{562−500c}$] prime factors, counted with the multiplicity. This result constitutes an improvement upon that of Tolev.
LI ZHU^{1} ^{}
Volume 131, 2021
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