Year: 2026
Type: preprint
Abstract: The study of the largest prime factor in polynomial sequences can be traced back at least to the late 19th century in the work of Störmer. Mahler (1933) and Chowla (1934) proved that the largest prime factor of $n^2+1$ grows at least as fast as $\log_2 n$. In 2023 we improved this to $(\log_2 n)^2/\log_3 n$. In this note we show the lower bound $(\log_2 n)^2/\log_4 n$, and that when this bound is nearly sharp it also holds for many prime factors of $n^2+1$.
Source: arXiv (Cornell University)
Author: Pasten, Hector
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7206178452