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# State/Multiplicativity of the totient

Proposition: (Multiplicativity of the totient) Suppose that $a$ and $b$ are positive integers, and $GCD(a,b) = 1$. Then the totient of the product of $a$ and $b$ equals the product of the totient of $a$ and the totient of $b$: $$\phi(ab) = \phi(a) \phi(b).$$

## Logical Connections

This statement logically relies on the following definitions and statements: Def/Totient, State/Being relatively prime to a product is equivalent to being relatively prime to the factors, State/Chinese remainder theorem

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