Question

For $n>1$, let $H$ be the set of all products in $S_n$ of a multiple of four transpositions. Show $H=A_n$.

score 107 · Answer 1 · 2026-04-14 16:20:39

107

Views

For $n>1$, let $H$ be the set of all products in $S_n$ of a multiple of four transpositions. Show $H=A_n$.

Published on 14 Apr 2026 - 16:20

score 747 · Answer 2 · 2026-04-17 15:33:36

747

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How to prove that for all real number $x$, $x+ \frac{1}{x} \geq 2$

Published on 17 Apr 2026 - 15:33

score 476 · Answer 3 · 2026-04-14 10:42:13

476

Views

Every finite field has an extension in which every element has a square root

Published on 14 Apr 2026 - 10:42

score 18 · Answer 4 · 2026-04-16 12:13:51

18

Views

Find the minimum and maximum values for variables from two equations

Published on 16 Apr 2026 - 12:13

score 463 · Answer 5 · 2026-04-16 16:00:21

463

Views

$ Av=\lambda v \implies\ A^*v=\overline \lambda v $, Is this true only for normal operators?

Published on 16 Apr 2026 - 16:00

score 65 · Answer 6 · 2026-04-17 05:01:07

65

Views

How to prove $a_1 = 2$, $a_2 = 4$ and $a_{n+1} = \frac{1}{3}(2a_n+a_{n-1})$ for all $n \geq2$

Published on 17 Apr 2026 - 5:01

score 101 · Answer 7 · 2026-04-16 07:30:33

101

Views

prove or disprove: If $c > 0$ and $a < b < c $ , then $a \not \equiv b$ mod $c$

Published on 16 Apr 2026 - 7:30

score 413 · Answer 8 · 2026-04-15 11:31:45

413

Views

Prove by induction that $\sum_{i=1}^n \frac{1}{\sqrt i} > \sqrt n$ for all integers $n \ge 2$

Published on 15 Apr 2026 - 11:31

score 265 · Answer 9 · 2026-04-16 21:08:22

265

Views

Quotient map and connected sets proof

Published on 16 Apr 2026 - 21:08

score 252 · Answer 10 · 2026-04-16 00:31:56

252

Views

if $x \equiv y$ (mod $m$), then $ax^2 + bx + c \equiv ay^2 + by + c$ (mod $m$)

Published on 16 Apr 2026 - 0:31

score 109 · Answer 11 · 2026-04-15 06:13:20

109

Views

Ordering integer multiplets

Published on 15 Apr 2026 - 6:13

score 49 · Answer 12 · 2026-04-13 09:54:02

49

Views

Is this a correct proof of the closure proposition for subsets of a powerset?

Published on 13 Apr 2026 - 9:54

score 159 · Answer 13 · 2026-04-15 23:43:10

159

Views

Concluding whether $(y_n)_n$ is a bounded sequence

Published on 15 Apr 2026 - 23:43

score 76 · Answer 14 · 2026-04-13 17:16:45

76

Views

Proof verification. Show $x_{n+1} = 1 + {b\over x_n}$ diverges if $b < -{1\over 4}$

Published on 13 Apr 2026 - 17:16

score 78 · Answer 15 · 2026-04-15 16:18:21

78

Views

Proof by induction: $3^n|a_n\ $

Published on 15 Apr 2026 - 16:18

List Question

For $n>1$, let $H$ be the set of all products in $S_n$ of a multiple of four transpositions. Show $H=A_n$.

How to prove that for all real number $x$, $x+ \frac{1}{x} \geq 2$

Every finite field has an extension in which every element has a square root

Find the minimum and maximum values for variables from two equations

$ Av=\lambda v \implies\ A^*v=\overline \lambda v $, Is this true only for normal operators?

How to prove $a_1 = 2$, $a_2 = 4$ and $a_{n+1} = \frac{1}{3}(2a_n+a_{n-1})$ for all $n \geq2$

prove or disprove: If $c > 0$ and $a < b < c $ , then $a \not \equiv b$ mod $c$

Prove by induction that $\sum_{i=1}^n \frac{1}{\sqrt i} > \sqrt n$ for all integers $n \ge 2$

Quotient map and connected sets proof

if $x \equiv y$ (mod $m$), then $ax^2 + bx + c \equiv ay^2 + by + c$ (mod $m$)

Ordering integer multiplets

Is this a correct proof of the closure proposition for subsets of a powerset?

Concluding whether $(y_n)_n$ is a bounded sequence

Proof verification. Show $x_{n+1} = 1 + {b\over x_n}$ diverges if $b < -{1\over 4}$

Proof by induction: $3^n|a_n\ $

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