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# the function f(n)

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the function f(n) [#permalink]  28 Oct 2010, 08:27
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the function f is defined for all the 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 a prime number then f(p)?
a p-1
b p-2
c (p+1)/2
d (p-1)/2
e 2

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Re: the function f(n) [#permalink]  28 Oct 2010, 08:31
anilnandyala wrote:
the function f is defined for all the 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 a prime number then f(p)?
a p-1
b p-2
c (p+1)/2
d (p-1)/2
e 2

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.

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Re: the function f(n) [#permalink]  09 Nov 2010, 07:46
The moment you put a prime number in the function f(n), notice that all the numbers lesser than n have no divisor clashing with divisor of n since n is prime!!.

For instance f(7)= {6, 5, 4, 3, 2, 1}

Thus for f(p) number of integers falling under this set will be p-1

Re: the function f(n)   [#permalink] 09 Nov 2010, 07:46
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