Euler Phi Function of 152
Jump to navigation
Jump to search
Example of Use of Euler $\phi$ Function
- $\map \phi {152} = 72$
where $\phi$ denotes the Euler $\phi$ Function.
Proof
From Euler Phi Function of Integer:
- $\ds \map \phi n = n \prod_{p \mathop \divides n} \paren {1 - \frac 1 p}$
where $p \divides n$ denotes the primes which divide $n$.
We have that:
- $152 = 2^3 \times 19$
Thus:
\(\ds \map \phi {152}\) | \(=\) | \(\ds 152 \paren {1 - \dfrac 1 2} \paren {1 - \dfrac 1 {19} }\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 152 \times \frac 1 2 \times \frac {18} {19}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 4 \times 1 \times 18\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 72\) |
$\blacksquare$