Sums and differences of power-free numbers
Volume 169 / 2015
Acta Arithmetica 169 (2015), 169-180
MSC: Primary 11N25; Secondary 11N35.
DOI: 10.4064/aa169-2-4
Abstract
We employ a generalised version of Heath-Brown's square sieve in order to establish an asymptotic estimate of the number of solutions $a, b \in \mathbb N$ to the equations $a+b=n$ and $a-b=n$, where $a$ is $k$-free and $b$ is $l$-free. This is the first time that this problem has been studied with distinct powers $k$ and $l$.
