Question

Prove that if $p$ is a prime and $p\ne 2$, then $(\Bbb Z/p^n \Bbb Z)^*$ is cyclic

score 112 · Answer 1 · 2026-04-16 07:37:06

112

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Prove that if $p$ is a prime and $p\ne 2$, then $(\Bbb Z/p^n \Bbb Z)^*$ is cyclic

Published on 16 Apr 2026 - 7:37

score 140 · Answer 2 · 2026-04-15 00:23:25

140

Views

Show an explicit example concerning Primitive Element Theorem

Published on 15 Apr 2026 - 0:23

score 58 · Answer 3 · 2026-04-16 17:36:43

58

Views

Understanding $V=K\otimes_{\mathbb{F}_p}\mathbb{F}_{p^n}$ where $K$ is the algebraic closure of $\mathbb{F}_p$

Published on 16 Apr 2026 - 17:36

score 2.4k · Answer 4 · 2026-04-10 17:05:55

2.4k

Views

Galois group of polynomials over finite fields

Published on 10 Apr 2026 - 17:05

score 147 · Answer 5 · 2026-04-15 08:00:10

147

Views

Proving $F(\alpha)/F$ is a Galois extension, where $\alpha \in E \supset F$ is a root of $x^p-x-a=p(x) \in F[X]$, irreducible in $F$

Published on 15 Apr 2026 - 8:00

score 93 · Answer 6 · 2026-04-08 15:08:55

93

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Why $\mathbb{Z}[\theta]\,/\,\mathcal{P} \simeq \mathbb{F}_{p^e}$ for any non-zero prime ideal $\mathcal{P}$ of $\mathbb{Z}[\theta]$?

Published on 08 Apr 2026 - 15:08

score 69 · Answer 7 · 2026-04-14 21:31:51

69

Views

Bound for Number of $\mathbb{F}_q$-rational points on an elliptic curve

Published on 14 Apr 2026 - 21:31

score 195 · Answer 8 · 2026-04-13 16:28:52

195

Views

How many subﬁelds does a ﬁeld with $2^{36} = 68719476736$ elements have

Published on 13 Apr 2026 - 16:28

score 75 · Answer 9 · 2026-04-11 02:43:55

75

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Why $\mathbb{Z}[\theta]\,/\,\mathcal{P}$ is an algebraic extension over $\mathbb{Z}/p\mathbb{Z}$?

Published on 11 Apr 2026 - 2:43

score 1.1k · Answer 10 · 2026-04-16 15:50:49

1.1k

Views

Fields: Prove $1+1=0$

Published on 16 Apr 2026 - 15:50

score 74 · Answer 11 · 2026-04-11 20:44:51

74

Views

(From Milne) Splitting field over a finite field.

Published on 11 Apr 2026 - 20:44

score 93 · Answer 12 · 2026-04-12 00:41:28

93

Views

Prove $a+a=1$ using field table

Published on 12 Apr 2026 - 0:41

score 81 · Answer 13 · 2026-04-11 20:53:10

81

Views

$\mathfrak{sl}_n$ over finite commutative rings

Published on 11 Apr 2026 - 20:53

score 364 · Answer 14 · 2026-04-17 01:11:20

364

Views

Necessary and sufﬁcient conditions on m and n for $\Bbb F_{p^n}$ to have a subﬁeld isomorphic with $F_{p^m}$.

Published on 17 Apr 2026 - 1:11

score 1.7k · Answer 15 · 2026-04-16 04:50:05

1.7k

Views

Free distance of a convolutional code

Published on 16 Apr 2026 - 4:50

List Question

Prove that if $p$ is a prime and $p\ne 2$, then $(\Bbb Z/p^n \Bbb Z)^*$ is cyclic

Show an explicit example concerning Primitive Element Theorem

Understanding $V=K\otimes_{\mathbb{F}_p}\mathbb{F}_{p^n}$ where $K$ is the algebraic closure of $\mathbb{F}_p$

Galois group of polynomials over finite fields

Proving $F(\alpha)/F$ is a Galois extension, where $\alpha \in E \supset F$ is a root of $x^p-x-a=p(x) \in F[X]$, irreducible in $F$

Why $\mathbb{Z}[\theta]\,/\,\mathcal{P} \simeq \mathbb{F}_{p^e}$ for any non-zero prime ideal $\mathcal{P}$ of $\mathbb{Z}[\theta]$?

Bound for Number of $\mathbb{F}_q$-rational points on an elliptic curve

How many subﬁelds does a ﬁeld with $2^{36} = 68719476736$ elements have

Why $\mathbb{Z}[\theta]\,/\,\mathcal{P}$ is an algebraic extension over $\mathbb{Z}/p\mathbb{Z}$?

Fields: Prove $1+1=0$

(From Milne) Splitting field over a finite field.

Prove $a+a=1$ using field table

$\mathfrak{sl}_n$ over finite commutative rings

Necessary and sufﬁcient conditions on m and n for $\Bbb F_{p^n}$ to have a subﬁeld isomorphic with $F_{p^m}$.

Free distance of a convolutional code

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