Euler Phi Function of 4
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Example of Use of Euler $\phi$ Function
- $\map \phi 4 = 2$
where $\phi$ denotes the Euler $\phi$ function.
Proof
From Euler Phi Function of Prime Power: Corollary:
- $\map \phi {2^k} = 2^{k - 1}$
Thus:
- $\map \phi 4 = \map \phi {2^2} = 2^1 = 2$
They can be enumerated as:
- $1, 3$
$\blacksquare$
Sources
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.4$: Integer Functions and Elementary Number Theory: Exercise $27$