Determine the order of $Z_8/ \langle [3] \rangle$
Ok, I feel like I'm missing something very simple. The order of $Z_8$ is 8. The order of $\langle [3] \rangle$ is 3. But 8/3 does not divide evenly. What am I missing?
2026-03-31 08:45:32.1774946732
Determine the order of $Z_8/ \langle [3] \rangle$
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I think $[3]$ might actually refer to the set of elements of $\mathbb Z_8$ generated by $3$. If this is the case, then the order of $[3]$ is equal to $2$, since $3^2 \equiv 1\bmod 8$, implying that $[3]=\{1,3\}$.