Exercise 2.1.2 (First examples, part 2)

Question

Exhibit a complete residue system modulo $17$ composed entirely of multiples of $3$.

Richard Ganaye · Accepted Answer

\begin{proof} Since $3\wedge 17 = 1$,
$$\{0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48\}$$
is a complete residue system modulo $17$ composed entirely of multiples of $3$.

(Reduced modulo $17$, this gives
$$\{0, 3, 6, 9, 12, 15, 1, 4, 7, 10, 13, 16, 2, 5, 8, 11, 14\}.)$$
\end{proof}

Exercise 2.1.2 (First examples, part 2)

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Exercise 2.1.2 (First examples, part 2)

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