On an tangent equation by primes

S. I. Dimitrov

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arXiv · 2111.02933

On an tangent equation by primes

S. I. Dimitrov

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Abstract

In this paper we introduce a new diophantine equation with prime numbers. Let $[\, \cdot\,]$ be the floor function. We prove that when $1 1$ is a fixed, then every sufficiently large positive integer $N$ can be represented in the form \begin{equation*} N=\big[p^c_1\tan^\theta(\log p_1)\big]+ \big[p^c_2\tan^\theta(\log p_2)\big]+ \big[p^c_3\tan^\theta(\log p_3)\big]\,, \end{equation*} where $p_1,\, p_2,\, p_3$ are prime numbers. We also establish an asymptotic formula for the number of such representations.

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BibTeX RIS

S. I. Dimitrov. 2021-11-04. On an tangent equation by primes. https://arxiv.org/abs/2111.02933

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