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The function F is defined for all positive integers n by the

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The function F is defined for all positive integers n by the [#permalink]

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New post 24 Jan 2010, 18:38
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The function F is defined for all positive integers n by the following rule: f(n) is the number of position integer each of which is less than n, and has no position 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
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Apr 2014, 06:27, edited 1 time in total.
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Re: Function question [#permalink]

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New post 24 Jan 2010, 19:41
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bhavinnc wrote:
The function F is defined for all position integers n by the following rule: f(n) is the number of position integer each of which is less than n, and has no position 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

please some one explain how the correct answer is a)
thanks


I hope I interpreted your question correctly:
1. f(n) is the number of positive integers less than n
2. f(n) has no positive factor in common with n, other than 1

f(p), where p is prime:
Take p=7:
a) 7 -1 = 6, which works for 1 and 2 above.
b) 7-2 = 5, which does not work for 1 above --- there are 6 positive integers less than 7
c) (7+1)/2=4, which again does not work for 1.
d) (7-1)/2=3, again does not work for 1.
e) 2, again does not work for 1.
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Re: Function question [#permalink]

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New post 24 Jan 2010, 22:36
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bhavinnc wrote:
The function F is defined for all position integers n by the following rule: f(n) is the number of position integer each of which is less than n, and has no position 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

please some one explain how the correct answer is a)
thanks


The confusing moment in this question is its wording. Basically question is: how many positive integers are less than given prime number p which has no common factor with p except 1.

Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).

If we consider p=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-1=6.

Answer: A.
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Re: Function question [#permalink]

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New post 27 Jan 2010, 16:45
Hi,
Originally i had typo there, its not position but i should write positive.

But thanks, both of you for great explanation.

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Re: Function question [#permalink]

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New post 28 Jan 2010, 12:55
bhavinnc,

Thanks for humor with positive and position...!

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Re: The function F is defined for all positive integers n by the [#permalink]

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Re: The function F is defined for all positive integers n by the [#permalink]

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New post 28 Jul 2016, 22:39
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Re: The function F is defined for all positive integers n by the   [#permalink] 28 Jul 2016, 22:39
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