Pairs of square-free values of the type ${\mathbf{n}}^2+1$, ${\mathbf{n}}^2+2$

Abstract

In the present paper we show that there exist infinitely many consecutive square-free numbers of the form $n^2+1$, $n^2+2$. We also establish an asymptotic formula for the number of such square-free pairs when $n$ does not exceed given sufficiently large positive integer.

References in corpus (2)

• Pairs of k-free Numbers, consecutive square-full Numbers
• Consecutive square-free values of the form $[\alpha \mathbf{p}],[\alpha \mathbf{p}]+1$