Euler Phi Function/Examples/9
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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: $\text{(iii)}$