Received February 5, 2022. Published online November 16, 2022.
Abstract: We use the estimation of the number of integers $n$ such that $\lfloor n^c \rfloor$ belongs to an arithmetic progression to study the coprimality of integers in $\mathbb{N}^c=\{ \lfloor n^c \rfloor\}_{n\in\mathbb{N}}$, $c>1$, $c\notin\mathbb{N}$.
Keywords: greatest common divisor; natural density; Piatetski-Shapiro sequence
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Affiliations: Watcharapon Pimsert, Teerapat Srichan (corresponding author), Department of Mathematics, Faculty of Science, Kasetsart University, 50 Ngamwongwan Rd, Lat Yao, Chatuchak, Bangkok 10900, Thailand, e-mail: fsciwcrp@ku.ac.th, fscitrp@ku.ac.th; Pinthira Tangsupphathawat, Department of Mathematics, Faculty of Science and Technology, Phranakorn Rajabhat University, 9 Changwattana Road, Bangkhen Bangkok, 10220, Thailand, e-mail: t.pinthira@hotmail.com
