The Euler phi-function is defined for positive integers n by (n) = s, where s is the number of positive integers less than or equal

The Euler phi-function is defined for positive integers n by φ(n) = s, where s is the number of positive integers less than or equal ton that are relatively prime ton. Use Exercise 45 to show that

the sum being taken over all positive integers d dividing n. 

Data from Exercise 45

Show that a finite cyclic group of order n has exactly one subgroup of each order d dividing n, and that these are all the subgroups it has.

- ), din H =