Euler Phi Function of 5002
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Example of Euler $\phi$ Function of Square-Free Integer
- $\map \phi {5002} = 2400$
where $\phi$ denotes the Euler $\phi$ Function.
Proof
From Euler Phi Function of Square-Free Integer:
- $\ds \map \phi n = \prod_{\substack {p \mathop \divides n \\ p \mathop > 2} } \paren {p - 1}$
where $p \divides n$ denotes the primes which divide $n$.
We have that:
- $5002 = 2 \times 41 \times 61$
and so is square-free.
Thus:
\(\ds \map \phi {5002}\) | \(=\) | \(\ds \paren {2 - 1} \paren {41 - 1} \paren {61 - 1}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 40 \times 60\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2400\) |
$\blacksquare$