Exercise 2.1.3 (First examples, part 3)

Question

Exhibit a reduced residue system for the modulus $12$; for $30$.

Richard Ganaye · Accepted Answer

\begin{proof} $\phi(12) = 4.$

Modulo $12$,  a reduced residue system is 
$$\{1, 5,7,11\}.$$

$\phi(30)= 8$.

Modulo $30$,  a reduced residue system is 
$$\{1, 7, 11, 13, 17, 19, 23, 29\}.$$

Python:
\begin{verbatim}
[a for a in range(30) if gcd(a,30) == 1]
\end{verbatim}

Answers