Let denote Euler’s totient function. Prove that for it holds that:

where stands for the Riemann zeta function.

**Solution**

Well by Euler’s product we have,

thus,

(1)

and

(2)

Combining we get the result.

**Note: **It also holds that

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Let denote Euler’s totient function. Prove that for it holds that:

where stands for the Riemann zeta function.

**Solution**

Well by Euler’s product we have,

thus,

(1)

and

(2)

Combining we get the result.

**Note: **It also holds that