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Let be a measurable set with no integer distances, that is, such that for any distinct . How large can the measure of be?
Source: erdosproblems.com/953
No claim settles this problem.
Open. The site keeps the label OPEN, and its curator has not commented on Chojecki's upper bound. That bound, which with the lower bound the site credits settles the exponent , is an accepted partial result recorded on its claim page (Chojecki, 2026); the constant-factor question is open.