Largest Prime Factors of Polynomials

2023/08/19 by N. A. Carella, Carella, N. A.
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #Primary 11N05 #Secondary 11N32

paper · pdf · doi:10.48550/arxiv.2308.10075

openalex publication_date 2023/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let x>1 be a large number. This note shows that the largest prime factor of the quadratic product ∏_{x≤ n≤ 2x}(n²+1 ) satisfies the relation p ≥ x^3/2 as x tends to infinity. This improves the current estimate p ≥ x^1.279.

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