Euler Phi Function of 1798

Example of Euler $\phi$ Function of Square-Free Integer

$\map \phi {1798} = 840$

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:

$1798 = 2 \times 29 \times 31$

and so is square-free.

Thus:

\(\ds \map \phi {1798}\)

\(=\)

\(\ds \paren {29 - 1} \paren {31 - 1}\)

\(\ds \)

\(=\)

\(\ds 28 \times 30\)

\(\ds \)

\(=\)

\(\ds 840\)

$\blacksquare$