(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find eight elements [itex]r \in \mathbb{Q}[x]/(x^4-16)[/itex] such that [itex]r^2=r[/itex].

2. Relevant equations

N/A

3. The attempt at a solution

The elements [itex]0+(x^4-16)[/itex] and [itex]1+(x^4-16)[/itex] clearly satisfy the desired properties, but I still need six more elements. Can anyone help me figure out a technique for finding a few more elements?

Thanks!

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# Homework Help: Polynomial Rings

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