Author

D. Krachun

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Preprint Aug 2026

Square-Difference-Free Sets beyond the Three-Quarter Barrier

Let $D(N)$ denote the largest cardinality of a subset of $\{1,\ldots,N\}$ containing no nonzero square difference. While a construction certifying $D(N)\geq (1-o(1))N^{1/2}$ is almost trivial, Erd\H{o}s conjectured that this bound is sharp up to polylogarithmic factors. This was disproved by S\'ark\"ozy and later again...

D. Krachun · 1 citation