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Math Help - multiplicative functions

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    Last edited by alyssams; August 4th 2012 at 05:21 PM.
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  2. #2
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    Re: multiplicative functions

    Quote Originally Posted by alyssams View Post
    I know that given m, n with gcd(m,n)=1 you can split k into two relatively prime factors in a suitable way depending on m and n.
    Anyway, help is appreciated!
    How do you know that the domain is the set of integers?

    If f is multiplicative, then f(k)f(n) = f(kn) for all k,n. Then f(n) = \frac{f(kn)}{f(k)}, which is also multiplicative. Also we know that f(k) \neq 0 so we don't have to worry about dividing by zero or anything like that...
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