List questions from finite-fields

Published on 24 Mar 2026 - 20:36

432

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Prove every finite field is of cardinality $p^n$

Published on 16 Jan 2019 - 15:51

331

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Generating random (torsion) point on elliptic curve efficiently

Published on 25 Mar 2026 - 23:36

69

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Can we have two different polynomials of the same degree $d$ here in the factorisation of $x^{p^n} -x$?

Published on 27 Mar 2026 - 18:09

50

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Cardinality of a field between interval

Published on 17 Jan 2019 - 18:13

79

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Invertible elements of $\mathbb{Z}_3[x] / (x^4+x^3-1)^3$

Published on 26 Mar 2026 - 12:07

1.8k

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Characteristic and primitive roots of unity

Published on 18 Jan 2019 - 8:49

547

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Help on solutions of the congruence $f(x)=x^3+4x+8 \equiv 0 \pmod {15}$

Published on 18 Jan 2019 - 10:28

255

Views

Separability in a finite field

Published on 18 Jan 2019 - 17:17

33

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On trinomials over finite fields

Published on 19 Jan 2019 - 20:27

239

Views

Show that $K$ is a field

Published on 20 Jan 2019 - 11:24

52

Views

Prove that each element of polynomial ring with irreducible characteristic has exactly one minimum polynomial.

Published on 20 Jan 2019 - 21:34

625

Views

Element of given order in a finite field

Published on 23 Jan 2019 - 7:31

72

Views

Condition for roots of $x^2+xy+y^2\in\mathbb{F}_{q^n}[x,y]$

Published on 23 Jan 2019 - 9:19

57

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Linear dependency in certain fields

Published on 23 Jan 2019 - 13:43

List Question

Computing the zeta function of curves over finite fields.

Prove every finite field is of cardinality $p^n$

Generating random (torsion) point on elliptic curve efficiently

Can we have two different polynomials of the same degree $d$ here in the factorisation of $x^{p^n} -x$?

Cardinality of a field between interval

Invertible elements of $\mathbb{Z}_3[x] / (x^4+x^3-1)^3$

Characteristic and primitive roots of unity

Help on solutions of the congruence $f(x)=x^3+4x+8 \equiv 0 \pmod {15}$

Separability in a finite field

On trinomials over finite fields

Show that $K$ is a field

Prove that each element of polynomial ring with irreducible characteristic has exactly one minimum polynomial.

Element of given order in a finite field

Condition for roots of $x^2+xy+y^2\in\mathbb{F}_{q^n}[x,y]$

Linear dependency in certain fields

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