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Math Help - Help with euler-phi function

  1. #1
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    Help with euler-phi function

    Hi can someone help me with this question,

    "Give a brief argument to show that phi(n) is even for all n>2"
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  2. #2
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    Quote Originally Posted by BruceBronson View Post
    Hi can someone help me with this question,

    "Give a brief argument to show that phi(n) is even for all n>2"
    If \gcd(a,b)=1 then \phi(ab)=1. If n>1 and p an odd prime divisor of it we can write n=p^kj where j not divisible by p. Then \phi(n) = \phi(p^k)\phi(j). Thus, \phi (p^k) = p^{k}-p^{k-1} which is even. Now finish the argument.

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