The function f is defined for all positive integers n by the following 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 number then f(p) =
(a) p-1
(b) p-2
(c) (p+1)/2
(d) (p-1)/2
(e) 2
The OA is A.
Can any expert explain this PS question please? I don't have it clear. Thanks.
Hi LUANDATO,
Let's take a look at your question.
The question statement should be like:
The function f is defined for all positive integers n by the following 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 then f(p) = ?
The function is defined as:
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 a prime number let's say 5,
f(p) will contain the number of positive integers less than 5,
It means f(p) will contain 4 positive integers less than 5 i.e. {1, 2, 3, 4}
We can see that all of these four numbers have only factor in common with 5 i.e. 1. No factor other than 1 is common between these four numbers and 5.
Therefore, f(p) = p - 1
If p = 5, f(p) will contain 4 positive integers. i.e. f(p) = 5-1 = 4
Similarly, if p = 11, f(p) will contain 10 positive integers. i.e. f(p) = 11 - 1 = 10
Therefore, Option
A is correct.
Hope this helps.
I am available, if you'd like any follow up.
