2025/08/04 by Tsz Ho Chan, Laura Holmes, Chan, Tsz Ho +5
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2508.02818
openalex publication_date 2025/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study numbers n that can be factored in four different ways as n = A B = (A + a1) (B - b1) = (A + a2) (B - b2) = (A + a3) (B - b3) with B ≤ A, 1 ≤ a1 < a2 < a3 ≤ C and 1 ≤ b1 < b2 < b3 ≤ C. We obtain the optimal upper bound A ≤ 0.04742 … ⋅ C3 + O(C). The key idea is to transform the original question into generalized Pell equations a x2 - b y2 = c and study their solutions.