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(Solved): Let f(n)=(1)n1. 1. Prove that f is multiplicative. 2. Prove that ( ...


Let \( f(n)=(-1)^{n-1} \). 1. Prove that \( f * \mu \) is multiplicative. 2. Prove that \( (f * \mu)\left(p^{e}\right)=0 \) f???????

Let . 1. Prove that is multiplicative. 2. Prove that for an odd prime and . 3. Prove that for . 4. Prove that for .


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Solution:1To prove the properties of the function f(n) = (?1)n?1,we will use the following:f(n) is multiplicative: If gcd(m,n) = 1, then f(mn) = f(m)
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