IMO Shortlist 2006 problem N2


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2. travnja 2012.
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For x \in (0, 1) let y \in (0, 1) be the number whose n-th digit after the decimal point is the 2^{n}-th digit after the decimal point of x. Show that if x is rational then so is y.
Izvor: Međunarodna matematička olimpijada, shortlist 2006