On a Logarithmic Equation by Primes

S. I. Dimitrov ()
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S. I. Dimitrov: Technical University of Sofia

A chapter in Approximation and Computation in Science and Engineering, 2022, pp 217-226 from Springer

Abstract: 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 = [ p 1 log p 1 ] + [ p 2 log p 2 ] + [ p 3 log p 3 ] , $$\displaystyle N=[p_1\log p_1]+[p_2\log p_2]+[p_3\log p_3], $$ where p1, p2, andp3 are prime numbers. We also establish an asymptotic formula for the number of such representations, when p1, p2, andp3 do not exceed given sufficiently large positive number.

Keywords: Diophantine equation; Logarithmic equation; Primes; 11P32; 11P55 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-84122-5_12

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DOI: 10.1007/978-3-030-84122-5_12

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