On an equation involving fractional powers with prime numbers of a\n special type

2017/05/21 by Zhivko Petrov, Petrov, Zhivko
Mathematics · #11P05 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1705.07484

openalex publication_date 2017/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the equation [p₁^c] + [p₂^c] + [p₃^c] = N, where\nN is a sufficiently large integer, and prove that if 1 < c < \(17)/(16),\nthen it has a solution in prime numbers p₁, p₂, p₃ such that\neach of the numbers p₁ + 2, p₂ + 2, p₃ + 2 has at most [\n\(95)/(17 - 16c) ] prime factors, counted with the multiplicity.\n

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