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arXiv · 2306.12431

On the sum of two powered numbers

Jörg Brüdern·Olivier Robert
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Abstract

Fix a positive real number $\theta$. The natural numbers $m$ with largest square-free divisor not exceeding $m^\theta$ form a set $\mathscr{A}$, say. It is shown that whenever $\theta>1/2$ then all large natural numbers $n$ are the sum of two elements of $\mathscr{A}$. This is nearly best possible.

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Jörg Brüdern, Olivier Robert. 2023-06-09. On the sum of two powered numbers. https://arxiv.org/abs/2306.12431

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