Geodesic
Sums and differences of power-free numbers
Julia Brandes 1
1 Mathematisches Institut Bunsenstr. 3–5 37073 Göttingen, Germany
Acta Arithmetica, Tome 169 (2015) no. 2, pp. 169-180 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $l$.
DOI : 10.4064/aa169-2-4
Keywords: employ generalised version heath browns square sieve order establish asymptotic estimate number solutions mathbb equations a b where k free l free first time problem has studied distinct powers

Julia Brandes  1

1 Mathematisches Institut Bunsenstr. 3–5 37073 Göttingen, Germany 
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Julia Brandes. Sums and differences of power-free numbers. Acta Arithmetica, Tome 169 (2015) no. 2, pp. 169-180. doi: 10.4064/aa169-2-4

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