Question

How many elements of order $7$ are there in a group of order $28$ without Sylow's theorem?

score 1.2k · Answer 1 · 2013-05-08 04:50:00

1.2k

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How many elements of order $7$ are there in a group of order $28$ without Sylow's theorem?

Published on 08 May 2013 - 4:50

score 3.2k · Answer 2 · 2013-05-10 15:15:00

3.2k

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Proving $\sum_{k=1}^n{k^2}=\frac{n(n+1)(2n+1)}{6}$ without induction

Published on 10 May 2013 - 15:15

score 982 · Answer 3 · 2013-05-19 19:13:21

982

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The unity of a subdomain

Published on 19 May 2013 - 19:13

score 1.5k · Answer 4 · 2013-05-24 15:42:00

1.5k

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Proof of the equality of the difference of two sets iff sets are equal (direct vs. indirect)

Published on 24 May 2013 - 15:42

score 5.1k · Answer 5 · 2026-03-30 17:38:15

5.1k

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Surprisingly elementary and direct proofs

Published on 30 Mar 2026 - 17:38

score 1.9k · Answer 6 · 2013-05-29 10:47:16

1.9k

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Using Nakayama's Lemma to prove isomorphism theorem for finitely generated free modules

Published on 29 May 2013 - 10:47

score 283 · Answer 7 · 2013-06-02 04:48:54

283

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Combinatorial proof of the fact $p$ doesn't divide $ n \choose p^k$

Published on 02 Jun 2013 - 4:48

score 519 · Answer 8 · 2013-06-03 12:32:33

519

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$\sum a+b+c \sum \frac{ab+bc+ca}{a+b+c} \sum \frac{abc}{ab+bc+ca} \leq \sum a \sum b \sum c$

Published on 03 Jun 2013 - 12:32

score 1k · Answer 9 · 2013-06-05 11:36:49

1k

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Prove: if $f(x) =x\sin (\pi x)$ then $f'(x)$ vanishes at a unique point in $ ( n + 1/2, n) $

Published on 05 Jun 2013 - 11:36

score 4.3k · Answer 10 · 2026-03-28 06:23:25

4.3k

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Why are only fractions with denominator 2 and 5 non-repeating?

Published on 28 Mar 2026 - 6:23

score 431 · Answer 11 · 2013-06-08 14:45:31

431

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How many values of $x$ are there such that $\sqrt{x(x+p)}$ is a positive integer for some $p$?

Published on 08 Jun 2013 - 14:45

score 108 · Answer 12 · 2013-06-18 14:51:23

108

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Proofs that $f^{(100)}(0)= -\frac1{101}$, where $f(x) = \frac{\sin x}x$ and $f(0)=1$

Published on 18 Jun 2013 - 14:51

score 580 · Answer 13 · 2026-03-27 16:54:10

580

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A few standard results (on metrizability and relative separation strength) without choice?

Published on 27 Mar 2026 - 16:54

score 602 · Answer 14 · 2026-04-08 22:20:46

602

Views

Pólya and Szegő, Part I, Ch. 4, 174.

Published on 08 Apr 2026 - 22:20

score 271 · Answer 15 · 2013-06-23 14:14:52

271

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Prove $\frac{\cos^2 A}{1 - \sin A} = 1 + \sin A$ by the Pythagorean theorem.

Published on 23 Jun 2013 - 14:14

List Question

How many elements of order $7$ are there in a group of order $28$ without Sylow's theorem?

Proving $\sum_{k=1}^n{k^2}=\frac{n(n+1)(2n+1)}{6}$ without induction

The unity of a subdomain

Proof of the equality of the difference of two sets iff sets are equal (direct vs. indirect)

Surprisingly elementary and direct proofs

Using Nakayama's Lemma to prove isomorphism theorem for finitely generated free modules

Combinatorial proof of the fact $p$ doesn't divide $ n \choose p^k$

$\sum a+b+c \sum \frac{ab+bc+ca}{a+b+c} \sum \frac{abc}{ab+bc+ca} \leq \sum a \sum b \sum c$

Prove: if $f(x) =x\sin (\pi x)$ then $f'(x)$ vanishes at a unique point in $ ( n + 1/2, n) $

Why are only fractions with denominator 2 and 5 non-repeating?

How many values of $x$ are there such that $\sqrt{x(x+p)}$ is a positive integer for some $p$?

Proofs that $f^{(100)}(0)= -\frac1{101}$, where $f(x) = \frac{\sin x}x$ and $f(0)=1$

A few standard results (on metrizability and relative separation strength) without choice?

Pólya and Szegő, Part I, Ch. 4, 174.

Prove $\frac{\cos^2 A}{1 - \sin A} = 1 + \sin A$ by the Pythagorean theorem.

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