On an tangent equation by primes

2021/11/04 by S. I. Dimitrov, Dimitrov, S. I.
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2111.02933

openalex publication_date 2021/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce a new diophantine equation with prime numbers. Let [ ⋅ ] be the floor function. We prove that when 11 is a fixed, then every sufficiently large positive integer N can be represented in the form N=[p^c₁tan^θ(log p₁)]+ [p^c₂tan^θ(log p₂)]+ [p^c₃tan^θ(log p₃)] , where p₁, p₂, p₃ are prime numbers. We also establish an asymptotic formula for the number of such representations.

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