Additive Representations of Natural Numbers

Forrest J. Francis, Ethan S. Lee

Published 2020-03-18Version 1

We establish an improved lower bound for a weighted counting function of representations of $n$ as the sum of a prime and a square-free number and provide several applications for this bound. These applications are generalisations of a result of Dudek, which states that every natural number greater than 2 may be written as the sum of a prime and a square-free number.