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{\bf{\centerline{ Math 431 Problem Set 7}}}


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{\bf 1.} Ex 19.1\smallskip

{\bf2.} Ex 20.1 \smallskip 

{\bf 3.} Ex 20.3 
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  {\bf{4.}} Ex 20.4 \smallskip



 {\bf 5.} Ex 20.5 \smallskip

{\bf 6.} Ex 21.1 \smallskip

{\bf 7.} Ex 21.2\smallskip

{\bf 8.} Ex 21.3

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{\bf Exploration: Multiplicative Functions}
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{\bf 8.} Let $f(n)$ be a multiplicative function and $F(n)=\sum_{d\vert
n,d>0}f(d)$. \smallskip (a) Show that one can solve to express $f(n)$ in
terms of the values of
$F(d)$ for $d\vert n$. For example, $f(12)=F(12)-F(6)-F(4)+F(2)$.\smallskip
(b) Try to find the numbers $c_{n,d}$ such that $f(n)=\sum_{d\vert
n, d>0} c_{n,d}F(d)$\smallskip\bye