I have question about Number Theory ! which are :

(i) Let g be an arithmetic multiplicative function with g(1) = 1. Show that the functiondeﬁned by

G(n): =∑ d|n g(d)

is multiplicative.

(ii) Suppose that f is a multiplicative function, with f(1) = 1 and let µ denote the Mobius

function. Show that ∑ µ(d) f(d) = (1 -f(p1)) ..... (1 - f(pr))

Can you help me to solve these questions,please?

(i) Let g be an arithmetic multiplicative function with g(1) = 1. Show that the functiondeﬁned by

G(n): =∑ d|n g(d)

is multiplicative.

(ii) Suppose that f is a multiplicative function, with f(1) = 1 and let µ denote the Mobius

function. Show that ∑ µ(d) f(d) = (1 -f(p1)) ..... (1 - f(pr))

Can you help me to solve these questions,please?

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