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Determining whether or not an expression is multiplicative.

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Is this expression multiplicative? Justify your answer.

f(n)=1, n>1. Factor n into a product of primes,n=p1^k1*
p2^k2...
then set f(n)= (-1)^k1+k2+...+kr.

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Solution Summary

It is determined whether or not an expression is multiplicative. The expert factors products of prime functions.

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Yes it is.
We need to show f(n)f(m)=f(nm)
Given two integers n and m, suppose n=p1^k1*p2^k2*...*pr^kr,
m=q1^t1*q2^t2*...*qs^ts.
Then ...

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