Optimal bounds for Büchi's problem in modular arithmetic II
Year: 2019
Type: preprint
Abstract: Given a prime $p\ge5$ and an integer $s\ge1$, we show that there exists an integer $M$ such that for any quadratic polynomial $f$ with coefficients in the ring of integers modulo $p^s$, such that $f$ is not a square, if a sequence $(f(1),\dots,f(N))$ is a sequence of squares, then $N$ is at most $M$. We obtain this result by reducing to the case where $f$ has an invertible dominant coefficient.
Source: arXiv (Cornell University)
Authors: Sáez, Pablo, Vidaux, Xavier, Vsemirnov, Maxim
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951595756