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prime numbers

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prime numbers

by mkhanna » Thu Sep 24, 2009 8:31 am
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 prime, then f(p) =
a) P-1
b) P-2
c) (P+1)/2
d) (P-1)/2
e) 2
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by bdoug » Thu Sep 24, 2009 8:43 am
We are looking for the number of positive integers less than P that has no common factors except for 1

The problem gives us that P is a prime number, meaning it's only factors are P and 1, therefore, every positive integer less than P will be included in our answer, so we simply take P - 1 to get the number of positive integers less than P.

I found it a bit tricky when deciding whether to exclude the integer 1 (which would have given us P - 2 for the answer), but I decided to include it because it is a positive integer less than P with no common factors except for 1.
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by vivekjaiswal » Thu Sep 24, 2009 7:57 pm
bdoug wrote:We are looking for the number of positive integers less than P that has no common factors except for 1

The problem gives us that P is a prime number, meaning it's only factors are P and 1, therefore, every positive integer less than P will be included in our answer, so we simply take P - 1 to get the number of positive integers less than P.

I found it a bit tricky when deciding whether to exclude the integer 1 (which would have given us P - 2 for the answer), but I decided to include it because it is a positive integer less than P with no common factors except for 1.
Nice explanation, thanks bdoug
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