No, it does not say anything about the value of \varphi (p^{\alpha}) but wikipedia saves the day. O was reading Wolfram's Mathworld's proof but I got lost around here:
Here's the link.
http://mathworld.wolfram.com/TotientFunction.html
Hello.
I have been reading a book with an introductory section on number theory and the part regarding Euler's function just said that \varphi (n) = n-1 when n is prime and that \varphi (n) = n(1-\frac{1}{p_{1}})(1-\frac{1}{p_{2}})...(1-\frac{1}{p_{n}}) when n is a composite number.
The...
Okay, here's what I've thought:
We know that
a^{p-1} = a^{ke+r} = (a^e)^k a^r \equiv a^e \equiv 1 (\bmod \ p)
We also know that
a^e \equiv 1 (\bmod \ p) ,
we can infer from this that
(a^e)^n \equiv 1(\bmod p) for any integer n, thus the only way for
(a^e)^k a^r \equiv a^e...
Hello everyone, I have been trying to teach myself number theory and I am stuck trying to prove a (I am sure) very easy to prove theorem related to that of Fermat's.
The theorem I am to prove states:
Let e be the lowest number (natural) such that a^e \equiv 1 (\bmod \ p) for p prime such...