Euler Phi Function of 4

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 $27$