olymmath

ISL 2016 N2

  • Answer

Let τ(n)\tau(n) be the number of positive divisors of nn. Let τ1(n)\tau_{1}(n) be the number of positive divisors of nn which have remainders 1 when divided by 3 . Find all possible integral values of the fraction τ(10n)τ1(10n)\frac{\tau(10 n)}{\tau_{1}(10 n)}.

Dataset text NuminaMath olympiads. Quoted with source.

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2 \text{ or any composite number}

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