Sums and differences of power-free numbers

Julia Brandes

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arXiv · 1505.07031

Sums and differences of power-free numbers

Julia Brandes

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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 $l$.

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Julia Brandes. 2015-05-26. Sums and differences of power-free numbers. https://arxiv.org/abs/1505.07031

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