Primes of the form $[{n}^c]$ with  square-free $n$

S. I. Dimitrov

doi:10.3842/umzh.v76i2.7258

S. I. Dimitrov Faculty of Applied Mathematics and Informatics, Technical University of Sofia, Bulgaria

DOI: https://doi.org/10.3842/umzh.v76i2.7258

Keywords: Prime numbers $\cdot$ Square-free numbers $\cdot$ Exponential sums

Abstract

UDC 621

Let $[\, \cdot\,]$ be the floor function. We show that if $1<c<\dfrac{3849}{3334},$ then there exist infinitely many prime numbers of the form $[n^c],$ where $n$ is square-free.

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