# Search results

1. ### Proof of Euler's fuction.

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
2. ### Proof of Euler's fuction.

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...
3. ### Help with proof of theorem related to Fermat's.

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...
4. ### Help with proof of theorem related to Fermat's.

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...