S\'ark\"ozy's theorem in $\mathbf{F}_2[x]$

Aleksandra Kowalska

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arXiv · 2510.27573

S\'ark\"ozy's theorem in $\mathbf{F}_2[x]$

Aleksandra Kowalska

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Abstract

Green showed that, conditional on GRH, a subset $A \subseteq [N]$ with $\mid A \mid \gg_{\epsilon} N^{\frac{11}{12}+\epsilon}$ must contain two elements whose difference is $p-1$ for $p$ a prime. We prove an analogous unconditional result for $\mathbf{F}_2[x]$, improving the exponent to $\frac{7}{8}+\epsilon$.

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Aleksandra Kowalska. 2025-10-31. S\'ark\"ozy's theorem in $\mathbf{F}_2[x]$. https://arxiv.org/abs/2510.27573

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