1. ## euler phi function

Let n be within Z with n>0. Prove that the number of fractions a/b in lowest terms with 0<a/b1 and bn is

2. The factions are:

$x/1$, [1]
$x/2$, [2]
$x/3$, [3]
...
$x/n$. [4]

In [1] the number of reduced fractions is $\phi (1)$.
In [2] the number of reduced fractions is $\phi (2)$.
In [3] the number of reduced fractions is $\phi(3)$.
...
In [4] the number of reduced fractions is $\phi(n)$.

Thus, in total we have $\phi ( 1) + ... + \phi(n)$ such fractions.