- Introduction to Euler’s Totient Function
- Generalization of Fermat’s Theorem
- Totient Function of primes, $\varphi (p) \text{ and } \varphi (p^k)$
- Prove that, $\varphi (n)$ is a multiplicative function.
- Prove that,
$$
\begin{align*}
\phi(n) &= n \prod_{i=1}^{k} \left( 1 - \frac{1}{p_i} \right)
\end{align*}
$$
Exercises:
- Prove that $\varphi(n)$ is always even.
- Prove that, $a \mid b \implies \varphi(a) \mid \varphi(b)$