Roth's Theorem in Super Smooth Numbers
Number Theory
2025-10-22 v1
Abstract
We say that the set of -smooth numbers up to is super smooth if for a large fixed constant . We show that the Roth's theorem on arithmetic progressions is true in super smooth numbers case. This extends the result of Harper where he showed the statement is true under a weaker hypothesis.
Cite
@article{arxiv.2510.18024,
title = {Roth's Theorem in Super Smooth Numbers},
author = {Laurence P. Wijaya},
journal= {arXiv preprint arXiv:2510.18024},
year = {2025}
}