Shehzad Hathi, Daniel R. Johnston
Published 2021-09-24, updated 2023-11-24Version 2
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.
On the representation of integer as sum of a square-free number and a prime of special type
On the Sum of a Prime and a Square-free Number
Divisibility conditions on the order of the reductions of algebraic numbers
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