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Find the least n - ILL 1990 FRG1

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September 18, 2010
number theorybinary representationdecimal representationIMO ShortlistIMO Longlist

Problem Statement

Find, with proof, the least positive integer nn having the following property: in the binary representation of 1n\frac 1n, all the binary representations of 1,2,…,19901, 2, \ldots, 1990 (each consist of consecutive digits) are appeared after the decimal point.
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