Ace test series

Question

The formula for the number of positive integers m which are less than p^k and relatively prime to p^k, where p is a prime number and k is a positive integer is__________-

A)p^k(p-1)                                                                                       B)(p^(k-2))(p-1)

C)p^k(p-2)                                                                                       D)(p^(k-1))(p-1)

Answer 1

By the property

$\phi (n) = n.(1-\frac{1}{P_1}).(1-\frac{1}{P_2})......(1-\frac{1}{P_n})$

$m = \phi(P^k)$

     $ = P^k (1-\frac{1}{P})$

     $ = P^{k-1} (P-1)$

So answers should be D