Exercise 2.1.32 (Other complete residue system)

Question

Show that $2,4,6,\ldots,2m$ is a complete residue system modulo $m$ if $m$ is odd.

Richard Ganaye · Accepted Answer

ewcommand{\Z}{\mathbb{Z}}

\begin{proof} By Theorem 2.6, since $m\wedge 2 = 1$, and $1,\ldots, m$ is a complete system of residue modulo $m$, then $2,4,6,\ldots,2m$ is a complete residue system modulo $m$ if $m$ is odd.
\end{proof}

\bigskip
(Note : It is the same to say that
$$
\left\{
\begin{array}{ccl}
\Z/m\Z& 	o & \Z/m\Z\
x & \mapsto & 2x
\end{array}
ight.
$$
is bijective if $m$ is odd.)

Exercise 2.1.32 (Other complete residue system)

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Exercise 2.1.32 (Other complete residue system)

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