Euler Phi Function of 256

Example of Use of Euler $\phi$ Function

The value of the Euler $\phi$ function for the integer $256$ is $128$.

Proof

From the corollary to Euler Phi Function of Prime Power:

$\phi \left({2^k}\right) = 2^{k-1}$

Thus:

\(\ds \phi \left({256}\right)\)

\(=\)

\(\ds \phi \left({2^8}\right)\)

\(\ds \)

\(=\)

\(\ds 2^7\)

\(\ds \)

\(=\)

\(\ds 128\)

$\blacksquare$