- #1
T-O7
- 55
- 0
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:
[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?
[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?