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 also has no positive factor in common with n other than 1. If p is a prime number then f(p) =
A) p-1
B) p-2
C) (p+1)/2
D) (p-1)/2
E) 2
Just plug in a prime number for p.
Let p = 5.
There are 4 positive integers less than 5 that have no factors in common with 5 other than 1: 1, 2, 3, 4.
So f(5) = 4. This is our target answer.
Now we plug p=5 into all the answers to see which gives us our target answer of 4.
Only answer choice A works:
p-1 = 5-1 = 4.
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