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Math Help - euler func

  1. #1
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    euler func

    Prove that phee(n) is even for any n greater than or equal to 3 (here phee(n) is the Euler phee-
    function).
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  2. #2
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    Quote Originally Posted by anncar View Post
    Prove that phee(n) is even for any n greater than or equal to 3 (here phee(n) is the Euler phee-
    function).
    What do you know about \phi ?

    If you know that for n=p_1^{k_1}.. p_r^{k_r} , then:

    \phi(n)=(p_1-1)p^{k_1-1}..(p_r-1)p^{k_r-1}.

    And it follows immeadiatly that if n>2 that \phi is even (as if it has an odd prime factor p_i, then (p_i-1) is even and so \phi(n) is even, or if it only has even prime factors then it is a power k of 2 greater than the first and 2^{k-1} is even)

    ZB
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