a basic tutorial about number theory

Disclaimer: the content of this blog is the key takeways and my personal thinking about slides written by Professor Dan Boneh and available in Coursera

Definition of Euler’s $phi$ function: for an integer $N$, $phi(N) = |Z^*_n|$

nullModular’s $e^{th}$ root

Let $p$ be a prime and $c in Z_p$

Def: $x in Z_p$, s.t. $x^e = c$ in $Z_p$ is called an $e^{th}$ root
Example:
$$
begin{align}
7^{1/3} &= 6 text{ in } mathbb{Z}{11} nonumber
3^{1/2} &= 5 text{ in } mathbb{Z}{11} nonumber
1^{1/3} &= 1 text{ in } mathbb{Z}_{11} nonumber
end{align}
$$