Question

Show that every irreducible polynomial in $\mathbb Z_p$ is a divisor of $x^{p^n}-x$ for some $n$.

score 774 · Answer 1 · 2026-04-14 21:46:10

774

Views

Show that every irreducible polynomial in $\mathbb Z_p$ is a divisor of $x^{p^n}-x$ for some $n$.

Published on 14 Apr 2026 - 21:46

score 228 · Answer 2 · 2026-04-11 08:58:58

228

Views

Theorem 15, Section 3.5 of Hoffman’s Linear Algebra

Published on 11 Apr 2026 - 8:58

score 98 · Answer 3 · 2026-04-13 09:35:17

98

Views

Theorem 16 Corollary 2, Section 3.5 of Hoffman’s Linear Algebra

Published on 13 Apr 2026 - 9:35

score 35 · Answer 4 · 2026-04-12 00:40:43

35

Views

Proof Verification for Almost Uniform Convergence implies Convergence in Measure

Published on 12 Apr 2026 - 0:40

score 136 · Answer 5 · 2026-04-13 07:31:44

136

Views

Have you come across this proof of the Pythagoras Theorem?

Published on 13 Apr 2026 - 7:31

score 157 · Answer 6 · 2026-04-16 04:57:52

157

Views

Let $G$ be a group, $H < G$, and $A_H=\{g\mid\bar{g}\subset H\}$ where $\bar{g}$ is the conjugacy class of $g$. Prove $A_H\lhd G$.

Published on 16 Apr 2026 - 4:57

score 76 · Answer 7 · 2026-04-15 10:04:28

76

Views

Assume $K$ is non-empty compact and $U$ open such that $K \subset U$. Then there is $\varepsilon > 0$ such that $K_{\varepsilon} \subset U$

Published on 15 Apr 2026 - 10:04

score 38 · Answer 8 · 2026-04-10 21:36:59

38

Views

Intersection of two circles using Theorem of Alternatives

Published on 10 Apr 2026 - 21:36

score 161 · Answer 9 · 2026-04-11 10:25:32

161

Views

What is another way to prove the least amount of pence, nickels, dimes and quarters that guarantees making any change exactly?

Published on 11 Apr 2026 - 10:25

score 198 · Answer 10 · 2026-04-11 02:46:21

198

Views

An alternative, formal proof that $(\lnot\forall xPx)\to(\exists y(\lnot Py)).$

Published on 11 Apr 2026 - 2:46

score 81 · Answer 11 · 2026-04-13 11:19:28

81

Views

Most efficient way to prove basic set equality?

Published on 13 Apr 2026 - 11:19

score 68 · Answer 12 · 2026-04-14 22:18:01

68

Views

A $\sigma$-algebra is complete w.r.t. the metric $d_{\mu}(A, B) := \mu(A \triangle B)$

Published on 14 Apr 2026 - 22:18

score 51 · Answer 13 · 2026-04-14 23:02:44

51

Views

Proving (directly) the equivalence between two definitions of a Fréchet or $T_1$ space.

Published on 14 Apr 2026 - 23:02

score 74 · Answer 14 · 2026-04-17 03:30:04

74

Views

Let $\varphi_n, \psi$ be simple functions such that $(\varphi_n)$ is increasing and $\psi\le\lim_n\varphi_n$. Then $\int\psi\le\lim_n \int \varphi_n$

Published on 17 Apr 2026 - 3:30

score 100 · Answer 15 · 2026-04-16 03:22:51

100

Views

$a,b,c \in \mathbb{R}^+, \dfrac{a}{a+7b}+\dfrac{b}{b+7c}+\dfrac{c}{c+7a} \geq \dfrac{3}{8}$

Published on 16 Apr 2026 - 3:22

List Question

Show that every irreducible polynomial in $\mathbb Z_p$ is a divisor of $x^{p^n}-x$ for some $n$.

Theorem 15, Section 3.5 of Hoffman’s Linear Algebra

Theorem 16 Corollary 2, Section 3.5 of Hoffman’s Linear Algebra

Proof Verification for Almost Uniform Convergence implies Convergence in Measure

Have you come across this proof of the Pythagoras Theorem?

Let $G$ be a group, $H < G$, and $A_H=\{g\mid\bar{g}\subset H\}$ where $\bar{g}$ is the conjugacy class of $g$. Prove $A_H\lhd G$.

Assume $K$ is non-empty compact and $U$ open such that $K \subset U$. Then there is $\varepsilon > 0$ such that $K_{\varepsilon} \subset U$

Intersection of two circles using Theorem of Alternatives

What is another way to prove the least amount of pence, nickels, dimes and quarters that guarantees making any change exactly?

An alternative, formal proof that $(\lnot\forall xPx)\to(\exists y(\lnot Py)).$

Most efficient way to prove basic set equality?

A $\sigma$-algebra is complete w.r.t. the metric $d_{\mu}(A, B) := \mu(A \triangle B)$

Proving (directly) the equivalence between two definitions of a Fréchet or $T_1$ space.

Let $\varphi_n, \psi$ be simple functions such that $(\varphi_n)$ is increasing and $\psi\le\lim_n\varphi_n$. Then $\int\psi\le\lim_n \int \varphi_n$

$a,b,c \in \mathbb{R}^+, \dfrac{a}{a+7b}+\dfrac{b}{b+7c}+\dfrac{c}{c+7a} \geq \dfrac{3}{8}$

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