Number theory - Möbius function
Published by Angel on Friday, February 19, 2010 - 02:20:52 - Filed under Notes, Number theory
I like this function a lot, proposition is not THAT interesting but whatevs
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Lets define the Möbius function as:
Proposition:
is multiplicative and 
Proof:
Let gcd(m,n)=1
If 
or 
Then 
If 
, 
, then
If n or m = 1 proof is clear.
Now, let 
, since is multiplicative then F(n) is multiplicative.
It is clear that 
Also:
.
( Möbius function is 0 on 
)
Now, if we use prime factorization on n, if n>1:
we can do this because F(n) is multiplicative.
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I <3 Möbius function
