Improved Bounds on Sarkozy's Theorem for Quadratic Polynomials

TL;DR

This paper extends bounds on the size of subsets of natural numbers avoiding differences of the form quadratic polynomials, broadening the scope of previous results on square differences.

Contribution

It introduces improved bounds for sets avoiding differences of a wider class of quadratic polynomials, generalizing Sarkozy's theorem.

Findings

Established new upper bounds for such subsets

Extended previous results from square differences to general quadratic polynomials

Enhanced understanding of polynomial difference avoidance in number sets

Abstract

We extend the best known bound on the largest subset of {1,2,...,N} with no square differences to the largest possible class of quadratic polynomials.