Möbius Function/Examples/4

Example of Möbius Function

For $n \in \Z_{>0}$, let $\map \mu n$ denote the Möbius function of $n$.

Then:

$\map \mu 4 = 0$


Proof

\(\ds 2\) \(=\) \(\ds 2^2\) Prime Decomposition of $4$
\(\ds \leadsto \ \ \) \(\ds \map \mu 4\) \(=\) \(\ds 0\) as $4$ is not square-free

$\blacksquare$


Sources

  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Möbius function
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.