Erdős's integer dilation approximation problem is resolved: sets with positive logarithmic density always contain distinct α, β with |nα−β| arbitrarily small.
Behrend, On sequences of numbers not divisible by another
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Erd\H{o}s's integer dilation approximation problem and GCD graphs
Erdős's integer dilation approximation problem is resolved: sets with positive logarithmic density always contain distinct α, β with |nα−β| arbitrarily small.