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Math Help - Suppose that every prime...

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    Suppose that every prime...

    Suppose that every prime dividing n also divides m. Prove that φ(mn) = nφ(m).
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    Quote Originally Posted by NikoBellic View Post
    Suppose that every prime dividing n also divides m. Prove that φ(mn) = nφ(m).

    This follows at once from the formula: if n=p_1^{a_1}\cdot p_2^{a_2}\cdot\ldots\cdot p_r^{a_r}\,,\,\,then\,\,\,\phi(n)=n\prod^r_{i=1}\l  eft(1-\frac{1}{p_i}\right) , p_i,\,a_i\in\mathbb{N}\,,\,\,p_i primes. But you can also do a counting argument.

    Tonio
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