Discover an Original Identity with Merten's Function

[MathNerd]

I don't know if this identity has been found before but I have never seen it before in my study of Merten's function, so I believe this to be original. I derived the following interesting identity involving Merten's function

[tex] \sum_{ 1 \leq n \leq p - 1 } M( \frac {p}{n} ) = 0, \ \forall \ p \ \epsilon \ \Re[/tex]

where M(x) is Merten's function.

Tell me your thoughs ...

 

[geraldmcgarvey]

Mertens function

See
http://mathworld.wolfram.com/MertensFunction.html
Sum n=1..x M(x/n) = 1 (Lehman 1960)

[How do you get the graphic version, do you submit it
in Latex format and this website does the rest?]

 

[Muzza]

geraldmcgarvey, you enclose it in [ tex] [ /tex] tags (no spaces though). You can also click on any LaTeX graphic to see the code that generated it.