Question

A hint on why if $c$ is not a square in $\mathbf{F}_p$, then $c^{(p - 1)/2} \equiv -1 \mod p$

score 65 · Answer 1 · 2026-04-15 07:12:18

65

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A hint on why if $c$ is not a square in $\mathbf{F}_p$, then $c^{(p - 1)/2} \equiv -1 \mod p$

Published on 15 Apr 2026 - 7:12

score 240 · Answer 2 · 2026-04-12 11:06:50

240

Views

Galois Field $2^3$ Multiplication of $111$ and $111$

Published on 12 Apr 2026 - 11:06

score 538 · Answer 3 · 2026-04-10 19:31:20

538

Views

Homogenous polynomial over finite field having only trivial zero

Published on 10 Apr 2026 - 19:31

score 526 · Answer 4 · 2026-04-12 19:01:17

526

Views

Finding the kernel and image of a linear transformation over the field $\Bbb Z_2$

Published on 12 Apr 2026 - 19:01

score 74 · Answer 5 · 2026-04-16 20:59:42

74

Views

Set with roots of $x^{p^{q}}-x$ is $\mathrm{GF}(p^q)$?

Published on 16 Apr 2026 - 20:59

score 56 · Answer 6 · 2026-04-16 19:09:21

56

Views

Find maximum rank vector

Published on 16 Apr 2026 - 19:09

score 222 · Answer 7 · 2026-04-13 11:25:27

222

Views

How to find multiplicative orders of all elements in field $\Bbb F$ (say $\Bbb F_{13}$)?

Published on 13 Apr 2026 - 11:25

score 46 · Answer 8 · 2026-04-16 15:02:19

46

Views

Minimum polynom of an element in $K=\mathbb{F}_5[x]/(x^2-2)$

Published on 16 Apr 2026 - 15:02

score 44 · Answer 9 · 2026-04-17 09:32:02

44

Views

Action of $\mathbb{F}_{p^2}^\times/\mathbb{F}_{p}^\times$ on $P^1(\mathbb{F}_p)$

Published on 17 Apr 2026 - 9:32

score 27 · Answer 10 · 2026-04-17 04:32:26

27

Views

Prove that the image $\alpha$ of $X$ in $\left(\mathbb{F}_3[X]/(X^3-X^2+1)\right)^{\times}$ is a generator

Published on 17 Apr 2026 - 4:32

score 1.7k · Answer 11 · 2026-04-14 06:21:09

1.7k

Views

Sum of the values of a polynomial over a finite field

Published on 14 Apr 2026 - 6:21

score 450 · Answer 12 · 2026-04-17 14:25:55

450

Views

Normal basis of $GF(2^m)$ over $GF(2)$

Published on 17 Apr 2026 - 14:25

score 75 · Answer 13 · 2026-04-16 22:47:49

75

Views

Existence of a certain nonzero vector in $\mathbb F_p ^{2p-1}$ with vanishing inner products with two given vectors

Published on 16 Apr 2026 - 22:47

score 126 · Answer 14 · 2026-04-15 23:27:07

126

Views

Prove that $E$ is a finite extension of $F$ and $[E:F] \leq n$.

Published on 15 Apr 2026 - 23:27

score 7.7k · Answer 15 · 2026-04-13 23:52:14

7.7k

Views

How to find minimal polynomial for an element in $\mbox{GF}(2^m)$?

Published on 13 Apr 2026 - 23:52

List Question

A hint on why if $c$ is not a square in $\mathbf{F}_p$, then $c^{(p - 1)/2} \equiv -1 \mod p$

Galois Field $2^3$ Multiplication of $111$ and $111$

Homogenous polynomial over finite field having only trivial zero

Finding the kernel and image of a linear transformation over the field $\Bbb Z_2$

Set with roots of $x^{p^{q}}-x$ is $\mathrm{GF}(p^q)$?

Find maximum rank vector

How to find multiplicative orders of all elements in field $\Bbb F$ (say $\Bbb F_{13}$)?

Minimum polynom of an element in $K=\mathbb{F}_5[x]/(x^2-2)$

Action of $\mathbb{F}_{p^2}^\times/\mathbb{F}_{p}^\times$ on $P^1(\mathbb{F}_p)$

Prove that the image $\alpha$ of $X$ in $\left(\mathbb{F}_3[X]/(X^3-X^2+1)\right)^{\times}$ is a generator

Sum of the values of a polynomial over a finite field

Normal basis of $GF(2^m)$ over $GF(2)$

Existence of a certain nonzero vector in $\mathbb F_p ^{2p-1}$ with vanishing inner products with two given vectors

Prove that $E$ is a finite extension of $F$ and $[E:F] \leq n$.

How to find minimal polynomial for an element in $\mbox{GF}(2^m)$?

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