On the sum of a prime and a square-free number co-prime to any integer with at most two prime factors

Ethan S. Lee; Rowan O'Clarey

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arXiv · 2506.11814

On the sum of a prime and a square-free number co-prime to any integer with at most two prime factors

Ethan S. Lee·Rowan O'Clarey

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Abstract

Every natural number greater than $2$ can be written as the sum of a prime and a square-free number, and recent work has imposed additional divisibility conditions on the square-free number. We overcome limitations in these works to prove new results on square-free numbers co-prime to any integer with up to two prime factors, which make the expected asymptotic results explicit.

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Ethan S. Lee, Rowan O'Clarey. 2025-06-13. On the sum of a prime and a square-free number co-prime to any integer with at most two prime factors. https://arxiv.org/abs/2506.11814

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