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Analytic Number Theory Question: Prove the following statements: 1.) The number of distinct prime factors (n) is additive and 2^ ( n ) is multiplicative.

Analytic Number Theory Question:

Prove the following statements:

1.) The number of distinct prime factors (n) is additive and 2^(n) is multiplicative.

2.) The total number of prime factors(n) is completely additive.

3.) The Liouville function(n) is completely multiplicative.

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