I'm having a lot of problem with this proof. it states:
let n be an integer with n>1. prove that the sum of all positive integers k with 1 <= k < n and (k, n)=1 is .5n PHI(n).
i've been trying to use the following lemma as it was suggested in the "hint" section of the book:
let m be a positive integer with m>2. if a is a positive integer less than m with (a, m) =1, then (m-1, m)=1.
from that, you know that for some r, (n-rk, n) =1 where 0 <= n-rk < k.
does anyone have any suggestions for this problem? thanks a lot.
2007-02-26
01:44:06
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1 answers
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asked by
Jesse
2
in
Mathematics