A new upper bound for sets with no square differences

COMPOSITIO MATHEMATICA（2022）

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摘要

We show that if A subset of {1,..., N} has no solutions to a - b = n(2) with a, b is an element of A and n >= 1, then vertical bar A vertical bar << N/(logN (c log log logN) for some absolute constant c > 0. This improves upon a result of Pintz, Steiger, and Szemeredi.

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关键词

additive combinatorics, squares, difference set, density increment

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