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easy problem, but still...

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easy problem, but still...

by nailyad » Sun Dec 20, 2009 1:43 pm
The function f is defined for all positive integers by the 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)=

The answer is p-1.

What is the best way to approach to this problem?
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by cbenk121 » Sun Dec 20, 2009 9:31 pm
nailyad wrote:The function f is defined for all positive integers by the 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)=

The answer is p-1.

What is the best way to approach to this problem?
Prime number, by definition, only has itself and 1 as a factor. Therefore, if f(n) is the # of pos integers less than n, then it would be equal to p-1. It won't be p-2, because "1" is allowable (...has no positive factor in common with n other than 1).
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