A tangent inequality over primes

S. I. Dimitrov

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arXiv · 2110.08539

A tangent inequality over primes

S. I. Dimitrov

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Abstract

In this paper we introduce a new diophantine inequality with prime numbers. Let $1 1$, every sufficiently large positive number $N$ and a small constant $\varepsilon>0$, the tangent inequality \begin{equation*} \big|p^c_1\tan^\theta(\log p_1)+ p^c_2\tan^\theta(\log p_2)+ p^c_3\tan^\theta(\log p_3) -N\big|<\varepsilon \end{equation*} has a solution in prime numbers $p_1,\,p_2,\,p_3$.

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S. I. Dimitrov. 2021-10-16. A tangent inequality over primes. https://arxiv.org/abs/2110.08539

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