Question

Prove that for prime $p \gt 2$, $(p - 1)^{p - 1} \equiv p+1 \pmod{p^2}$.

score 48 · Answer 1 · 2020-08-17 15:34:51

48

Views

Prove that for prime $p \gt 2$, $(p - 1)^{p - 1} \equiv p+1 \pmod{p^2}$.

Published on 17 Aug 2020 - 15:34

score 216 · Answer 2 · 2020-08-24 23:56:31

216

Views

The cyclic nature of group U(n)

Published on 24 Aug 2020 - 23:56

score 1k · Answer 3 · 2020-08-28 17:40:33

1k

Views

Show that every group of order 15 is cyclic using class equation.

Published on 28 Aug 2020 - 17:40

score 57 · Answer 4 · 2020-08-30 16:42:08

57

Views

Invertible elements in $Z/27Z$ form a cyclic group

Published on 30 Aug 2020 - 16:42

score 448 · Answer 5 · 2026-03-25 15:17:48

448

Views

Cyclic extensions of degree $n$ which contain a primitive $n$-th root of unity

Published on 25 Mar 2026 - 15:17

score 1.1k · Answer 6 · 2020-09-04 19:59:36

1.1k

Views

Listing order of all the elements in multiplicative group and all of its generators

Published on 04 Sep 2020 - 19:59

score 757 · Answer 7 · 2020-09-05 07:10:03

757

Views

How do I show that a finite group $G$ of order $n$ is cyclic if there is at most one subgroup of order $d$ for each $d\mid n$?

Published on 05 Sep 2020 - 7:10

score 161 · Answer 8 · 2020-09-05 16:34:56

161

Views

Show no two cyclic subgroups of $G$ will share common generators.

Published on 05 Sep 2020 - 16:34

score 110 · Answer 9 · 2026-03-29 22:29:53

110

Views

How to decide when the field $\mathbb{Q}(\sqrt{a})$ where $a>0$ can be embedded in a cyclic Galois extension of order 4 over $\mathbb{Q}$?

Published on 29 Mar 2026 - 22:29

score 212 · Answer 10 · 2020-09-13 22:54:17

212

Views

How many cyclic groups are there of order $p^3 q^2$, where $p$ and $q$ are different primes?

Published on 13 Sep 2020 - 22:54

score 172 · Answer 11 · 2020-09-15 19:38:02

172

Views

If $|G| = 10$ and $G$ is abelian, show that $G$ is cyclic

Published on 15 Sep 2020 - 19:38

score 96 · Answer 12 · 2020-09-15 21:05:29

96

Views

Weird patterns in order of sums of elements in cyclic groups

Published on 15 Sep 2020 - 21:05

score 75 · Answer 13 · 2020-09-15 23:19:12

75

Views

Do the all points in subgroup of an elliptic curve with prime order have the same order?

Published on 15 Sep 2020 - 23:19

score 104 · Answer 14 · 2026-03-25 17:42:01

104

Views

How to prove that there is not a monomorphism from Klein 4-group to $Z_6$(or a epimorphism from $Z_6$ to $V_4$)?

Published on 25 Mar 2026 - 17:42

score 75 · Answer 15 · 2026-03-30 05:00:04

75

Views

Relationships between the Orders of an element in a Cyclic group (multiplicative and additive) Relating to prime numbers

Published on 30 Mar 2026 - 5:00

List Question

Prove that for prime $p \gt 2$, $(p - 1)^{p - 1} \equiv p+1 \pmod{p^2}$.

The cyclic nature of group U(n)

Show that every group of order 15 is cyclic using class equation.

Invertible elements in $Z/27Z$ form a cyclic group

Cyclic extensions of degree $n$ which contain a primitive $n$-th root of unity

Listing order of all the elements in multiplicative group and all of its generators

How do I show that a finite group $G$ of order $n$ is cyclic if there is at most one subgroup of order $d$ for each $d\mid n$?

Show no two cyclic subgroups of $G$ will share common generators.

How to decide when the field $\mathbb{Q}(\sqrt{a})$ where $a>0$ can be embedded in a cyclic Galois extension of order 4 over $\mathbb{Q}$?

How many cyclic groups are there of order $p^3 q^2$, where $p$ and $q$ are different primes?

If $|G| = 10$ and $G$ is abelian, show that $G$ is cyclic

Weird patterns in order of sums of elements in cyclic groups

Do the all points in subgroup of an elliptic curve with prime order have the same order?

How to prove that there is not a monomorphism from Klein 4-group to $Z_6$(or a epimorphism from $Z_6$ to $V_4$)?

Relationships between the Orders of an element in a Cyclic group (multiplicative and additive) Relating to prime numbers

Trending Questions

Popular # Hahtags

Popular Questions