GPREP #3

[hardikrs]

The function f is defined for all positive integers n by the formula 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) = ?

1. p-1
2. p-2
3. (p+1)/2
4. (p-1)/2
5. 2

Please explain your answer. thanks

[3Gs]

f(2) has no 1
f(3) has nos 2,1

so f(p) has p-1 nos hence 1 is the answer

[vineejay]

Let us substitute values in this problem:
p= 2,3,5,7,11, 13............
f(p)= f(2) = 1
f(3) = 2
f(5)= 4
so the correct answer = 1