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Number Theory

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Dirichlet Convolution, True/False

NUMTH-VKE1YB

Dirichlet convolution of two arithmetic functions $f$ and $g$ is defined by:

$$ f \ast g = \sum_{d|n} f(d) g\left(\frac nd\right) $$

Which of the following statements are true?

Select ALL that apply.

A

The operation $\ast$ is associative.

B

The operation $\ast$ is commutative.

C

The operation $\ast$ is not associative.

D

The operation $\ast$ is not commutative.

E

None of the above.