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

• Date: 2024
• Main Author: Dimitrov, S. I.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2024
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/7258
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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.