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The dyadic case of the Erdős similarity conjecture

OpenAI

OpenAI Mathopenai-math/The-dyadic-case-of-the-Erdos-similarity-conjectureSep 25, 2026math.CAAI-generatedscore 0

We construct a compact subset of the unit interval, of measure arbitrarily close to one, that contains no affine copy of the dyadic sequence $\{2^{-n}:n\ge1\}$. The conclusion holds for every translation and every nonzero real dilation, of either sign, proving the dyadic case of the Erdős similarity conjecture.

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