On an logarithmic equation by primes

2019/12/08 by S. I. Dimitrov, Dimitrov, S. I.
Mathematics · #Meromorphic and Entire Functions #Analytic Number Theory Research #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1912.03772

Abstract

Let [ ⋅ ] be the floor function. In this paper we show that every sufficiently large positive integer N can be represented in the form N=[p₁log p₁]+[p₂log p₂]+[p₃log p₃], where p₁, p₂, p₃ are prime numbers. We also establish an asymptotic formula for the number of such representations, when p₁, p₂, p₃ do not exceed given sufficiently large positive number.

Related

• On an tangent equation by primes
• On an equation with prime numbers close to squares
• On some problems of primes with the floor function
• On an equation by primes with one Linnik prime
• A logarithmic inequality involving prime numbers