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arXiv · 2109.11883

On the sum of a prime and a square-free number with divisibility conditions

Shehzad Hathi·Daniel R. Johnston
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Abstract

Every integer greater than two can be expressed as the sum of a prime and a square-free number. Expanding on recent work, we provide explicit and asymptotic results when divisibility conditions are imposed on the square-free number. For example, we show for odd $k\leq 10^5$ and even $k\leq 2\cdot 10^5$ that any even integer $n\geq 40$ can be expressed as the sum of a prime and a squarefree number coprime to $k$. We also discuss applications to other Goldbach-like problems.

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Shehzad Hathi, Daniel R. Johnston. 2021-09-24. On the sum of a prime and a square-free number with divisibility conditions. https://arxiv.org/abs/2109.11883

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