Dadidadida: $\varphi(1) = 1$

$\varphi(1) = 1$

But why ? Observe that

$\varphi(n)$ is equal to the number of integers between $0$ and $n-1$ that are relatively prime to $n$ .

Trivially,

$gcd(0,n) = n$ as

$n$ divides

$0$ , but

$gcd(0,n) = 1$ only when

$n = 1$ . In other words, zero is relatively prime to

$n$ only in the case when

$n = 1$ . Therefore, zero only counts in

$\lvert \mathbb{Z_1} \rvert$ .

$\Box$

# posted by rot13(Unafba Pune) @ 3:09 PM

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