mvictor wrote:

well damn...the wording is indeed confusing..as I was thinking that f(n) is the sum of the all numbers..

In such questions, it is advisable to take an example to figure out what the question is saying.

"The function f is defined for all the positive integers n by the following rule:"

We are looking at all positive integers so say n is 3.

"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 . "

Positive integers less than n -> 1, 2

Both do not have a factor in common with 3.

So f(n) = 2 (number of integers which have nothing in common with n except 1)

"if p is a prime number then f(p)?"

p must be a prime number. Our previous example was a prime number. Let's take another say 5.

Positive integers less than 5 -> 1, 2,3, 4

All 4 integers will have no factor in common with 5 because 5 is prime.

f(5) = 4

This will be the case with all prime numbers. Since a prime has no factor in common (except 1) with all positive integers less than it,

f(p) = p - 1

Answer (A)

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