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Math Help - 2 Problems

  1. #1
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    2 Problems

    Calculate  \varphi (n) for  n = 21^{21} and  n=2009 In each case, express the answer as the product of prime numbers

    Let a,b be natural numbers. Show that if  a|b then  \varphi (a)| \varphi (b)

    thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Jimmy_W View Post
    Calculate  \varphi (n) for  n = 21^{21} and  n=2009 In each case, express the answer as the product of prime numbers

    Let a,b be natural numbers. Show that if  a|b then  \varphi (a)| \varphi (b)

    thanks
    Here we assume that \varphi(n) denotes Euler's Totient function. In which case to answer this question you need the result that:

     <br />
\varphi(n)= (p_1-1)p_1^{k_1-1}(p_2-1)p_2^{k_2-1} .. (p_r-1)p_r^{k_r-1}<br />

    where n=p_1^{k_1} p_2^{k_2} .. p_r^{k_r} is the prime decomposition of n.

    CB
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