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arXiv · 2411.16069

On a multiplicative hybrid problem over almost-primes

Yuetong Zhao·Wenguang Zhai
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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.

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Yuetong Zhao, Wenguang Zhai. 2024-11-25. On a multiplicative hybrid problem over almost-primes. https://arxiv.org/abs/2411.16069

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