IMO Shortlist 1967 problem 2


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2. travnja 2012.
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Which fractions \displaystyle \dfrac{p}{q}, where p,q are positive integers < 100, is closest to \sqrt{2} ? Find all digits after the point in decimal representation of that fraction which coincide with digits in decimal representation of \sqrt{2} (without using any table).
Izvor: Međunarodna matematička olimpijada, shortlist 1967