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arXiv · 2011.13266

A new upper bound for sets with no square differences

Thomas F. Bloom·James Maynard
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Abstract

We show that if $A\subset \{1,\ldots,N\}$ has no solutions to $a-b=n^2$ with $a,b\in A$ and $n\geq 1$ then \[|A|\ll \frac{N}{(\log N)^{c\log\log \log N}}\] for some absolute constant $c>0$. This improves upon a result of Pintz-Steiger-Szemer\'edi.

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Thomas F. Bloom, James Maynard. 2020-11-26. A new upper bound for sets with no square differences. https://arxiv.org/abs/2011.13266

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