IMO Shortlist 2016 problem N2


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3. listopada 2019.
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Let \tau(n) be the number of positive divisors of n. Let \tau_1(n) be the number of positive divisors of n which have remainders 1 when divided by 3. Find all positive integral values of the fraction \frac{\tau(10n)}{\tau_1(10n)}.

Izvor: https://www.imo-official.org/problems/IMO2016SL.pdf