Sum Over Coprime Integers = 0 (or 1)
Leroy Quet
qq-quet at mindspring.com
Tue Aug 10 21:19:00 CEST 2004
Let the sequence {a(k)} be such that
a(1) = 1;
For each m >= 3,
0 = sum{1<=k<m,GCD(k,m)=1} a(k).
I get, by hand, the sequence beginning:
1, -1, -1, 1, -1, 1, 1, -1, -1,...
Is there a closed form for this sequence?
It is doubtful, especially since I only have 10 terms above, but could it
be that every term is either 1 or -1?
(I bet a counterexample, if one exists, is EASILY found.)
:)
thanks,
Leroy Quet
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