On the distribution of the greatest common divisor of the elements in integral part sets

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DOI:

https://doi.org/10.12697/ACUTM.2023.27.04

Keywords:

Beatty sequence, coprimality, floor function set, Piatetski–Shapiro sequence

Abstract

It is a classical result that the probability that two positive integers n, m ≤ x are relatively prime tends to 1/ζ(2) = 6/π2 as x → ∞. In this paper, the same result is still true when n and m are restricted to sub-sequences, i.e. Piatetski–Shapiro sequence, Beatty sequence and the floor function set.

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Author Biography

Teerapat Srichan, Kasetsart University

Department of Mathematics, Faculty of Science

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Published

2023-05-27

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Articles