Additive Representations of Natural Numbers

2020/03/18 by Forrest J. Francis, Francis, Forrest J., Ethan Simpson Lee +1 · 1 citation
Mathematics · #11Z05 #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2003.08083

openalex publication_date 2020/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Every natural number greater than two may be written as the sum of a prime and a square-free number. We establish several generalisations of this, by placing divisibility conditions on the square-free number.

Citations

• The ternary Goldbach conjecture is true
• Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅10¹⁸
• The large sieve
• Explicit Chen's theorem
• Sharper Bounds for the Chebyshev function θ(x)

Cited by

• An effective Bombieri-Vinogradov error term for sifting problems

Related

• Remarks on additive representations of natural numbers
• On the sum of a prime and an integer with divisibility restrictions
• On the Sum of a Prime and a Square-free Number
• Every integer can be written as a square plus a squarefree
• Additive problems with almost prime squares