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Improved bounds for the Furstenberg-S\'ark\"ozy theorem

Improved bounds for the Furstenberg-S\'ark\"ozy theorem

Suppose that $A \subset \{1,\dots, N\}$ has no two elements differing by a square. Then $|A| \ll N e^{-(\log N)^c}$ for any $c < \frac{1}{4}$.