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# The function f is defined for all positive integers n by the

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Manager
Joined: 17 Aug 2006
Posts: 86
The function f is defined for all positive integers n by the [#permalink]

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13 Nov 2008, 05:19
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 an prime number then f(p) =

p-1

p-2

(p+1)/2

(p-1)/2

2

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SVP
Joined: 17 Jun 2008
Posts: 1504

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13 Nov 2008, 05:50
p-2.

Since, p is a prime number, the only common factor between p and all positive integers less than p is 1.
Manager
Joined: 08 Aug 2008
Posts: 228

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13 Nov 2008, 11:13
$$P-1.$$

f(p) will be all numbers between 1 and P, inclusive of 1 and excluding P i.e. $$1<=f(p)<P$$
Manager
Joined: 23 Jul 2008
Posts: 189

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13 Nov 2008, 11:30
IMO A
p-1
f(2)=1
f(3)=2
f(5)=4
the only doubt i had with this one is whether to count 1 or not. I believe we should hence A
Manager
Joined: 16 Oct 2008
Posts: 54

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17 Nov 2008, 03:07
IMO A

I include 1 coz : f(n) is the number of positive integers each of which is less than n

what's OA

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Re: Prime f(p)   [#permalink] 17 Nov 2008, 03:07
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# The function f is defined for all positive integers n by the

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