Euler Phi Function/Examples/9

Example of Use of Euler $\phi$ Function

$\map \phi 9 = 6$

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


Proof

From Euler Phi Function of Prime Power:

$\map \phi {3^k} = 2 \times 3^{k - 1}$

Thus:

$\map \phi 9 = \map \phi {3^2} = 2 \times 3 = 6$

They can be enumerated as:

$1, 2, 4, 5, 7, 8$

$\blacksquare$


Sources

  • 1964: Walter Ledermann: Introduction to the Theory of Finite Groups (5th ed.) ... (previous) ... (next): Chapter $\text {I}$: The Group Concept: $\S 6$: Examples of Finite Groups: $\text{(iii)}$
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