List questions from finite-fields

Published on 24 Oct 2015 - 19:07

22

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How to evaluate this function in F_p efficiently?

Published on 25 Oct 2015 - 13:50

1.7k

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multiplication over gf(16)

Published on 25 Oct 2015 - 17:49

1.5k

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Show that multiplicative order mod p exists and that it divides (p-1)

Published on 25 Oct 2015 - 21:48

732

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Irreducibility of $f(x)=x^4-x^3+14x^2+5x+16$?

Published on 06 Apr 2026 - 0:22

121

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Proving that a Finite Field Over Its Prime Field Is Galois

Published on 26 Oct 2015 - 14:51

395

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gcd of two polynomials over the gf(2^4)

Published on 03 Apr 2026 - 12:53

58

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find out what $[\mathbb{Q}(a^2 + 2)/ \mathbb{Q} ] $ when $a$ satisfies $\alpha^6 - 3 \alpha^3 - 6 = 0$

Published on 29 Oct 2015 - 11:21

2.4k

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Let $(F,+,\cdot)$ is the finite field with $9$ elements. Then which of the following are true?

Published on 04 Apr 2026 - 12:01

150

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Confusion between vector space, field and sets

Published on 30 Oct 2015 - 15:25

106

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Show that $a^3+a+1$ is in the subfield $L$ with $4$ elements of the field $K=F_2[X]/(X^4+X^3+1)$

Published on 31 Oct 2015 - 20:14

422

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If $\phi$ : $F_2[X]/(X^3+X+1)$ $\rightarrow$ $F_2[X]/(X^3+X^2+1)$ is an isomorphism, then prove that $\phi(a)=b+1$, with $a$, $b$ the classes of $X$

Published on 04 Apr 2026 - 13:43

35

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Are $\mathbb{F}_{p^{d-1}} \subset \mathbb{F}_{p^d}$ Galois Extensions?

Published on 01 Nov 2015 - 20:11

479

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Calculating the generator of a Finite Field

Published on 29 Mar 2026 - 10:11

338

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How do finite fields work?

Published on 03 Nov 2015 - 21:28

List Question

Solving a quadratic equation in $\Bbb{Z}/19\Bbb{Z}$.

How to evaluate this function in F_p efficiently?

multiplication over gf(16)

Show that multiplicative order mod p exists and that it divides (p-1)

Irreducibility of $f(x)=x^4-x^3+14x^2+5x+16$?

Proving that a Finite Field Over Its Prime Field Is Galois

gcd of two polynomials over the gf(2^4)

find out what $[\mathbb{Q}(a^2 + 2)/ \mathbb{Q} ] $ when $a$ satisfies $\alpha^6 - 3 \alpha^3 - 6 = 0$

Let $(F,+,\cdot)$ is the finite field with $9$ elements. Then which of the following are true?

Confusion between vector space, field and sets

Show that $a^3+a+1$ is in the subfield $L$ with $4$ elements of the field $K=F_2[X]/(X^4+X^3+1)$

If $\phi$ : $F_2[X]/(X^3+X+1)$ $\rightarrow$ $F_2[X]/(X^3+X^2+1)$ is an isomorphism, then prove that $\phi(a)=b+1$, with $a$, $b$ the classes of $X$

Are $\mathbb{F}_{p^{d-1}} \subset \mathbb{F}_{p^d}$ Galois Extensions?

Calculating the generator of a Finite Field

How do finite fields work?

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