Two dimensional arithmetic progressions avoiding squares
Abstract
We show that any proper symmetric two dimensional arithmetic progression contained in the interval [-T,T] which avoids non-zero perfect squares has at most O(T20/27+) elements. This improves on a result of Croot, Lyall and Rice. We also discuss lower bounds for this problem and their connections to bounds for the least quadratic non-residue modulo a prime.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.