Question

For which prime $p$, is the group units $R^*$ cyclic?

score 94 · Answer 1 · 2026-04-15 08:37:33

94

Views

For which prime $p$, is the group units $R^*$ cyclic?

Published on 15 Apr 2026 - 8:37

score 114 · Answer 2 · 2026-04-14 20:22:35

114

Views

Formal derivative vs Little Fermat

Published on 14 Apr 2026 - 20:22

score 112 · Answer 3 · 2026-04-11 14:34:01

112

Views

Why it is sufficient to look at prime divisor of $p-1$ when finding generators of $\mathbb{Z}_p^*$?

Published on 11 Apr 2026 - 14:34

score 47 · Answer 4 · 2026-04-11 18:14:24

47

Views

Can you check my proof of finite fields are not algebraically closed?

Published on 11 Apr 2026 - 18:14

score 219 · Answer 5 · 2026-04-17 03:43:32

219

Views

Prove $Q_{mp} = Q_{m}(x^p)$ when prime $p$ divides $m$. ($Q$ is cyclotomic polynomial over some finite field $K$)

Published on 17 Apr 2026 - 3:43

score 738 · Answer 6 · 2026-05-04 12:23:12

738

Views

Prove that a field is a vector space over a subfield

Published on 04 May 2026 - 12:23

score 111 · Answer 7 · 2026-04-15 00:00:40

111

Views

When is a sum of various roots of unity a square in a finite field?

Published on 15 Apr 2026 - 0:00

score 213 · Answer 8 · 2026-04-15 04:22:30

213

Views

Polynomial over a finite field is a composition of a separable polynomial and a $x^{p^e}$.

Published on 15 Apr 2026 - 4:22

score 100 · Answer 9 · 2026-04-16 13:04:11

100

Views

Find all prime fields

Published on 16 Apr 2026 - 13:04

score 98 · Answer 10 · 2026-04-17 08:46:13

98

Views

Is there any difference between matrices over field with characteristic $0$ and over prime characteristic (particularly over $3$)?

Published on 17 Apr 2026 - 8:46

score 94 · Answer 11 · 2026-04-10 13:26:55

94

Views

Algorithm for generating Kakeya Sets in Finite Fields

Published on 10 Apr 2026 - 13:26

score 59 · Answer 12 · 2026-04-16 03:14:15

59

Views

Number of $2\times 2$ matrices $X$ such that $X^2 \equiv I \mod p$

Published on 16 Apr 2026 - 3:14

score 196 · Answer 13 · 2026-04-13 16:12:44

196

Views

Can the root of an irreducible polynomial be the root of a lower degree polynomial as well?

Published on 13 Apr 2026 - 16:12

score 1.7k · Answer 14 · 2026-03-25 23:38:28

1.7k

Views

Counting the number of similar matrices over finite fields

Published on 25 Mar 2026 - 23:38

score 163 · Answer 15 · 2026-04-16 10:10:11

163

Views

Let $f(x)=x^4+x^3+4x-1\in\mathbb{Z}_5[x]$. Let $K$ be the splitting field of $f$ over $\mathbb{Z}_5[x]$. Find $\mathrm{Gal}(K/\mathbb{Z}_5)$.

Published on 16 Apr 2026 - 10:10

List Question

For which prime $p$, is the group units $R^*$ cyclic?

Formal derivative vs Little Fermat

Why it is sufficient to look at prime divisor of $p-1$ when finding generators of $\mathbb{Z}_p^*$?

Can you check my proof of finite fields are not algebraically closed?

Prove $Q_{mp} = Q_{m}(x^p)$ when prime $p$ divides $m$. ($Q$ is cyclotomic polynomial over some finite field $K$)

Prove that a field is a vector space over a subfield

When is a sum of various roots of unity a square in a finite field?

Polynomial over a finite field is a composition of a separable polynomial and a $x^{p^e}$.

Find all prime fields

Is there any difference between matrices over field with characteristic $0$ and over prime characteristic (particularly over $3$)?

Algorithm for generating Kakeya Sets in Finite Fields

Number of $2\times 2$ matrices $X$ such that $X^2 \equiv I \mod p$

Can the root of an irreducible polynomial be the root of a lower degree polynomial as well?

Counting the number of similar matrices over finite fields

Let $f(x)=x^4+x^3+4x-1\in\mathbb{Z}_5[x]$. Let $K$ be the splitting field of $f$ over $\mathbb{Z}_5[x]$. Find $\mathrm{Gal}(K/\mathbb{Z}_5)$.

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