A conjecture of Yu and Chen related to the Erdős–Lewin theorem
Tom 217 / 2025
Acta Arithmetica 217 (2025), 277-286
MSC: Primary 11B13; Secondary 06A05
DOI: 10.4064/aa240108-20-6
Opublikowany online: 22 November 2024
Streszczenie
Yu and Chen (2022) conjectured that there exists a constant such that every integer n\ge 2 can be represented as a sum of integers of the form 2^\alpha 3^\beta , all of which are greater than cn/\log n and none of which divides any other. This conjecture strengthens a theorem of Erdős and Lewin, and the lower bound in the above conjecture is optimal up to a constant. The purpose of this paper is to prove this conjecture.
