The function f is defined for all positive integrers n by

Question

The function f is defined for all positive integrers 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) - 

a) p - 1
b) p - 2
c) (p+1)/2
d) (p-1)/2
e) 2

bkk145 · Answer

A.
Any prime won't have any factor other than itself and 1. So the number should be p-1.

ywilfred · Answer

f(11) = 10 (# of integers less than 11 and has no positive factors in common with n other than 1)
f(5) =4 (# of integers less than 5 and has no positive factors in common with n other than 1)

So f(p) = p-1

pmenon · Answer

the question says that f(n) is number of positive integers less than n that have factors in common ....

so, when considering the primes, which have just itself and 1 as a factor, shouldnt the answer really be p-2, because we cannot count p ... right ?

IrinaOK · Answer

I agree, actually, according to my calculations ALL the answer choices are correct, cuz there are no restrictions on the number of the intengers other than each must be less than p and have only one common divisor 1.

IrinaOK · Answer

I agree, actually, according to my calculations  ALL  the answer choices are correct, cuz there are no restrictions on the number of the intengers other than each must be less than p and have only one common divisor 1.

f.e: try p= 7

then,

f(7) can be 

A) 1,2,3,4,5,6
B) 1,2,3,4,5
C) 1,2,3,4
D) 1,2,3
E) 1

all satisfy the conditions, correct me please if I miss something

what is OA anyways?

The function f is defined for all positive integrers n by

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