Exercise 0.3.6 (squares in $\mathbb{Z}/4\mathbb{Z}$)

Question

Prove that the squares of the elements in $\mathbb{Z}/4\mathbb{Z}$ are just $\overline{0}$ and $\overline{1}$.

Richard Ganaye · Accepted Answer

\begin{proof} 
The square of the elements in $\mathbb{Z}/4\mathbb{Z} = \{\overline{0}, \overline{1},\overline{2},\overline{3}\}$ are 
$$\overline{0}^2 = \overline{0},\qquad \overline{1}^2 = \overline{1},\qquad \overline{2}^2 = \overline{4} = \overline{0}, \qquad \overline{3}^2 = \overline{-1}^2 = \overline{1}.$$
So the squares of the elements in $\mathbb{Z}/4\mathbb{Z}$ are just $\overline{0}$ and $\overline{1}$.


\end{proof}

Exercise 0.3.6 (squares in $\mathbb{Z}/4\mathbb{Z}$)

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Exercise 0.3.6 (squares in $\mathbb{Z}/4\mathbb{Z}$)

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