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Math Help - the Euler φ-function

  1. #1
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    the Euler φ-function

    Let x and y be integers; gcd(x,y)=g

    Prove that,

    φ(xy) = φ(x)φ(y)g/φ(g).
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  2. #2
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    Quote Originally Posted by swallenberg View Post
    Let x and y be integers; gcd(x,y)=g

    Prove that,

    φ(xy) = φ(x)φ(y)g/φ(g).

    try to use the fact that if gdc(m,n) = 1 then φ(mn) = φ(m)φ(n) and
    φ(n) = product of (1-1/pi), where pi is a prime that divides n.

    I think this should help...
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