Euler Phi Function/Examples/16

Example of Use of Euler $\phi$ Function

$\map \phi {16} = 8$

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


Proof

From the corollary to Euler Phi Function of Prime Power:

$\map \phi {2^k} = 2^{k - 1}$

Thus:

$\map \phi {16} = \map \phi {2^4} = 2^3 = 8$

$\blacksquare$


Sources

  • 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.1$: Functions: Ponderable $2.1.1$
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