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phi function
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spx2
Yang-Mills Theory
Yang-Mills Theory


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#1
phi function

i would like you people to help me know everything there is to know about the phi function of euler

PostPosted: Fri Feb 18, 2005 1:02 pm  Back to top 
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RobertuX
Poincare Conjecture
Poincare Conjecture


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#2
Re: phi function

spx2 wrote:
i would like you people to help me know everything there is to know about the phi function of euler

Well, \varphi(n):=#\{1\le m\le n:\gcd(m,n)=1\} so, if p prime, then \varphi(p)=p-1, in general if \gcd(m,n)=1 then \varphi(m,n)=\varphi(m)\varphi(n), and in general if n=p_1^{a_1}\cdots p_r^{a_r} with p_j primes, then \varphi(n)=n\left(1-\frac 1{p_1}\right)\dots \left(1-\frac 1 {p_r}\right), in fact there are more interesting ptoperties, if you have interest in any in particular, ask us!.

Best regards.

Robertux the Crazy Math
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RobertuX against the PEOPLE WHO try to make other people to HATES Science

PostPosted: Fri Feb 18, 2005 4:24 pm  Back to top 
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Arne
Birch & Swinnerton Dyer
Birch & Swinnerton Dyer


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#3
You forgot the most important one:

m divides a^{\phi(m)} - 1 if (a, m) = 1

PostPosted: Fri Feb 25, 2005 8:44 am  Back to top 
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AntonioMainenti
Riemann Hypothesis
Riemann Hypothesis


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#4
http://mathworld.wolfram.com/TotientFunction.html

That site is good when you have a question like this. "I want to know about so-and-so." That site has just about everything you would need.
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"i already made like infinity of those at scout camp" - napoleon d.

PostPosted: Fri Feb 25, 2005 6:53 pm  Back to top 
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