The function f is defined for all integers n by the...

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The function f is defined for all integers n by the following rule. f(n) is the number of positive integers ecah of which is less than n and has no positive factor in common with n other than 1. If p is any prime, then f(p)=?

A. p-1
B. p-2
C. (p+1)/2
D. (p-1)/2
E. 2

The OA is A .

Guys, does this questions makes sense to anyone? I am struggling. Does it mean that:

f(n) is a list of positive integers. Am I right?

for e.g f(5) = 3,4.

I am stuck after this. Can any expert help me with this PS question please?

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by DavidG@VeritasPrep » Mon Nov 27, 2017 7:29 am
swerve wrote:The function f is defined for all integers n by the following rule. f(n) is the number of positive integers ecah of which is less than n and has no positive factor in common with n other than 1. If p is any prime, then f(p)=?

A. p-1
B. p-2
C. (p+1)/2
D. (p-1)/2
E. 2

The OA is A .

Guys, does this questions makes sense to anyone? I am struggling. Does it mean that:

f(n) is a list of positive integers. Am I right?

for e.g f(5) = 3,4.

I am stuck after this. Can any expert help me with this PS question please?
The idea is that f(n) = the number of integers that share no common factors with n other than 1. For example, you invoked f(5). So how many integers share no common factors with 5, aside from 1? Well, the integers that share no common factors with 5 would be 1, 2, 3, and 4, giving us a total of 4 numbers. So f(5) = 4. Now simply plug '5' in for 'p' in the answer choices, and see which gives you a value of '4.' The answer is A
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