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The phi-function
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| Submitted: Thu Aug 28 2003
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MATHS INVESTIGATION THE PHI-FUNCTION Luke Meredith 11 Yellow The Problem With any positive integer (n), the Phi Function of n is ?(n). The Phi number of n is the amount of numbers from 1to n (not including 1 or n) that do no share any common factors with n. If the two or more numbers share no common factor, then the numbers are co-prime. So to put this into practice, the ?(8) = 4. This is because the positive integers less than 8, which have no common factors other than 1 with 8 are 1,3,5,7. This shows 4 of them, which is how the phi number is worked out. Another example is ?(15) = 8. The numbers, which do not have any common factors with 8, from numbers 1 to 8 (excluding 1 and 8), are 1,2,4,6,7,8,11,13,14 = 8 of them. What I am trying to find out is a...
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