On a multiplicative hybrid problem over almost-primes
Number Theory
2024-11-26 v1
Abstract
Let N be a large enough natural number, A and B be subsets of {N+1, ... , 2N}. In this paper, we prove that there exists integers a, b with a belongs to A, b belongs to B such that ab=P_k^2 + O(P_k^{1-c}), where 0<c<1/2 and P_k denotes an almost-prime with at most k prime factors, counted with multiplicity.
Cite
@article{arxiv.2411.16069,
title = {On a multiplicative hybrid problem over almost-primes},
author = {Yuetong Zhao and Wenguang Zhai},
journal= {arXiv preprint arXiv:2411.16069},
year = {2024}
}
Comments
15 pages