Pairs of square-free values of the type $\mathbf{n^2+1}$, $\mathbf{n^2+2}$
Number Theory
2022-07-01 v2
Abstract
In the present paper we show that there exist infinitely many consecutive square-free numbers of the form , . We also establish an asymptotic formula for the number of such square-free pairs when does not exceed given sufficiently large positive integer.
Cite
@article{arxiv.2004.09975,
title = {Pairs of square-free values of the type $\mathbf{n^2+1}$, $\mathbf{n^2+2}$},
author = {S. I. Dimitrov},
journal= {arXiv preprint arXiv:2004.09975},
year = {2022}
}