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
The factions are:
, [1]
, [2]
, [3]
...
. [4]
In [1] the number of reduced fractions is .
In [2] the number of reduced fractions is .
In [3] the number of reduced fractions is .
...
In [4] the number of reduced fractions is .
Thus, in total we have such fractions.