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

2021/09/24 by Shehzad Hathi, Daniel R. Johnston, Hathi, Shehzad +1 · 1 citation
Mathematics · #11P32 (Primary) 11Y99 (Secondary) #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2109.11883

openalex publication_date 2021/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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≤ 10⁵ and even k≤ 2⋅ 10⁵ that any even integer n≥ 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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