Euler Phi Function of 6

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Example of Euler $\phi$ Function of Square-Free Integer

$\map \phi 6 = 2$

where $\phi$ denotes the Euler $\phi$ Function.


Proof

From Euler Phi Function of Square-Free Integer:

$\displaystyle \map \phi n = \prod_{\substack {p \mathop \divides n \\ p \mathop > 2} } \paren {p - 1}$

where $p \divides n$ denotes the primes which divide $n$.


We have that:

$6 = 2 \times 3$

and so is square-free.


Thus:

\(\displaystyle \map \phi 6\) \(=\) \(\displaystyle \paren {3 - 1}\)
\(\displaystyle \) \(=\) \(\displaystyle 2\)

$\blacksquare$