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EulerPhi[0] = 0?

Posted 11 years ago
Hello, 

How can it be that Phi(0) = 0? I thought it was only defined for positive integers. 


Regards, 

Dean Sparrow 
POSTED BY: Dean Sparrow
3 Replies
I see. Thanks for the information.
POSTED BY: Dean Sparrow
Bruce was right about this. The general context involves phi(-n) which is equal to phi(n). Thus phi(0) = 0 is a reasonable choice. Also 0 does not have a totative, so phi(0) should be zero. 
POSTED BY: Shenghui Yang
Multiple conventions?  See http://mathworld.wolfram.com/TotientFunction.html.

The Mathematica function EulerPhi is an implementation of phi(n) that handles zero and negative arguments in a convenient manner.  
POSTED BY: Bruce Miller
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