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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]  20 Feb 2006, 16:39
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 any prime number then f(p) =

a) 2

b) p/2 - 1/2

c) - (2-p)

d) -(1-p)

e) p/2 + 1/2
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Re: problem solving [#permalink]  20 Feb 2006, 17:51
Avis wrote:
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 any prime number then f(p) =

a) 2
b) p/2 - 1/2
c) - (2-p)
d) -(1-p)
e) p/2 + 1/2

looking for integers m such that
m < n
m is not a divisor of n
m != 1

p = 3
2 < 3, 2 is not a divisor of 3
f(3) = 1

p = 5
2 < 3 < 4 < 5, 2, 3, 4 are not divisors of 5
f(5) = 3

p = 7
2 < 3 ... 6 < 7, none of these are divisors of 7
f(7) = 5

Answer approx. f(p) = p - 2
p - 2 logical equivalent to - (2 - p)

(C)
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[#permalink]  21 Feb 2006, 05:00
good explanation.... , i was not able to do it !
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Director
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[#permalink]  21 Feb 2006, 07:19
As i look at the previous posts, i can't figure out why 1 is not counted. Can somebody shed some light?
thanks
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[#permalink]  21 Feb 2006, 07:43
Great explanation Zoelef.

Way2go
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[#permalink]  21 Feb 2006, 21:05
Should be D...

1 has to be included..
[#permalink] 21 Feb 2006, 21:05
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