I am asked to find the number of units in the quotient ring $\Bbb Z_5[x]/(x^4-1)$, where $\Bbb Z_5$ is the finite field consisting of 5 elements. I know that this ring has $5^4$ elements (which is not quite small), so I think I can't just do this using only computation. Any hints?
2026-04-02 01:35:36.1775093736
The number of units in the quotient ring $\Bbb Z_5[x]/(x^4-1)$
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Hint: Factor $x^4-1$ in $\Bbb Z_5[x]$ and use the Chinese remainder theorem.