On the difference between squares and integral $S$-units
Year: 2025
Type: article
Abstract: Let q_{1}, \ldots , q_{t} be distinct prime numbers. Let a_{1}, \ldots , a_{t} be nonnegative integers and x a positive integer. We establish an effective lower bound for the greatest prime divisor of |x^{2} - q_{1}^{a_1}\cdots q_{t}^{a_t}| , which tends to infinity with the maximum of x , a_{1}, \ldots , a_{t} .
Source: Portugaliae Mathematica
DOI: 10.4171/pm/2145
Author: Yann Bugeaud
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411276164