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> Find out an ideal $I$ of $\mathbb Z[x]$ suct that $\mathbb Z[x]/I$ is a field with 4 elements.
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[Here](https://math.stackexchange.com/questions/2381301/field-with-4-elements-mathbbzx-x2x1)  I get a similar question but I can not understand why $\mathbb Z[x]/(2,x^2+x+1)$ has only 4 elements. I just need to show the order is 4 . 

Please someone help ..

Thank you..

**Edit :** Now I have got the answer of it. It's because $\mathbb Z[x]/(2,x^2+x+1) \cong \mathbb Z\_2[x]/(x^2+x+1)$ and the later has only 4 elements.