So my job is to find a field with [tex]5^4[/tex] elements, and I know i can construct one by considering something of the form: [tex]F_5[x]/(x^4+bx^3+cx^2+1)[/tex]. So I thought i'd just consider this one:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]F_5[x]/(x^4+1)[/tex]

The problem is I'm not sure how to verify that this is indeed a field, i.e. i'm having trouble showing that a general non-zero element (which is of the form [tex]a+ b\alpha+c\alpha^2+d\alpha^3[/tex]) has an inverse. Does anyone know what to do?

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# Is this a field?

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