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The function f is define for all positive integers n by the

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New post 26 Feb 2006, 16:51
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The function f is define for all positive integers n by the folling 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) =
A. p-1
B. P-2
C. (P+1)/2
D. (P-1)/2
E. 2

Please explain.
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New post 26 Feb 2006, 18:36
If p is 2, f(p) = 1
If p is 3, f(p) = 2
If p is 5, f(p) = 3
If p is 7, f(p) = 4

I think C should fit in.
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New post 27 Feb 2006, 09:24
ywilfred wrote:
If p is 2, f(p) = 1
If p is 3, f(p) = 2
If p is 5, f(p) = 3
If p is 7, f(p) = 4

I think C should fit in.


isn't f(5)=4? 1, 2, 3, 4 all of which are less than 5 and has no positive factor in common with 5.

I think A
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New post 27 Feb 2006, 10:21
myc2004 wrote:
The function f is define for all positive integers n by the folling 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) =
A. p-1
B. P-2
C. (P+1)/2
D. (P-1)/2
E. 2

Please explain.


it's clearly that for every prime number p, there're (p-1) numbers from 1 to p-1 which has no common positive factors other than 1 with p.
To make it clearly:
1 and p have only 1 common (+) factor
2 and p have only 1 common (+) factor
.......................................................
(p-1) and p have only 1 common (+) factor.

Look at those provided answer choices:
1)p-2 and (p-1)/2 both are smaller than p-1 ...that means they don't indicate the maximum number of cases which satisfy the problem. ---> eliminate!
2) taking p=2 --> (p+1) is odd ---> (p+1)/2 is not integer ---> unreasonable ---> eliminate this choice
3) also take p=2 ---> f(p) = 1 ----> E can't be the OA

Only A left unbreakable ---> A it is.
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New post 27 Feb 2006, 14:48
OA is A thanks for explaining
  [#permalink] 27 Feb 2006, 14:48
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