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elements in Field such that $1+\alpha a^2+\beta b^2=0$

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#ring-theory #finite-fields
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How to determine the number of affine lines in

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#geometry #vector-spaces #finite-fields #affine-geometry
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Addition table for a finit field with 3 elements $\mathbb{F}_{3}=\{0,1,-1\}$

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#linear-algebra #finite-fields
71
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Is there a way to compute a exponentiation of $(X-1)$, without inversion?

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#matrices #finite-fields #exponentiation
70
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Quadratic Polynomials in $Z$ mod 3

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#elementary-number-theory #finite-fields
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Diagonalizability of symmetric bilinear forms over fields of characteristic $2$

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#linear-algebra #finite-fields #quadratic-forms #multilinear-algebra #bilinear-form
53
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Reducing a polynomial $ℤ\bmod 2$

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#finite-fields
133
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What is the Wedderburn decomposition of $\mathbb{F}_p[C_n]$?

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#ring-theory #representation-theory #finite-fields #cyclic-groups
642
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If $A$ is of characteristic $p$ :Then in $A[x]$ we have, $[a(x)+b(x)]^p=a(x)^p+b(x)^p$

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#abstract-algebra #ring-theory #finite-fields #group-isomorphism #frobenius-groups
1k
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Why does $x^n-1$ split over a finite field $\mathbb{F}_p$? (for $n|p-1$)

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#polynomials #modular-arithmetic #finite-fields #automorphism-group
40
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How many elements does the Field $Z_{5[x]}/f(x)$ have?

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#finite-fields
29
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Finding the inverse of (x-1) in $F=Z_{5} / (f(x))$

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#polynomials #finite-fields
1.1k
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Show that the Galois group of $ x^{p^n} − 2 $ over is $F_p$ is a cyclic group of order n.

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#field-theory #galois-theory #finite-fields
22
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Determining which field the polynomial $P(x)$ defines

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#finite-fields #irreducible-polynomials
105
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How to find the inverse of following matrix in $\mathbb Z/7 \mathbb Z$?

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#linear-algebra #matrices #finite-fields #congruences

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