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    OlympiadMediumNumber Theory10–12

    What is φ(15)\varphi(15) (Euler's totient)?

    Qual é φ(15)\varphi(15) (totiente de Euler)?

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    Solution

    φ(15)=15(1−13)(1−15)=15×23×45=8\varphi(15) = 15\left(1 - \tfrac{1}{3}\right)\left(1 - \tfrac{1}{5}\right) = 15 \times \tfrac{2}{3} \times \tfrac{4}{5} = 8.