myc2004 wrote:

The function f is define for all positive integers n by the folling rule: f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is any prime number than f(p) =

A. p-1

B. P-2

C. (P+1)/2

D. (P-1)/2

E. 2

Please explain.

it's clearly that for every prime number p, there're (p-1) numbers from 1 to p-1 which has no common positive factors other than 1 with p.

To make it clearly:

1 and p have only 1 common (+) factor

2 and p have only 1 common (+) factor

.......................................................

(p-1) and p have only 1 common (+) factor.

Look at those provided answer choices:

1)p-2 and (p-1)/2 both are smaller than p-1 ...that means they don't indicate the maximum number of cases which satisfy the problem. ---> eliminate!

2) taking p=2 --> (p+1) is odd ---> (p+1)/2 is not integer ---> unreasonable ---> eliminate this choice

3) also take p=2 ---> f(p) = 1 ----> E can't be the OA

Only A left unbreakable ---> A it is.