Question

For distinct primes $p$ and $q$, does any group of order $p^2q$ have a subgroup of order $p$ (without using Sylow or Cauchy)?

score 99 · Answer 1 · 2019-02-18 13:17:00

99

Views

For distinct primes $p$ and $q$, does any group of order $p^2q$ have a subgroup of order $p$ (without using Sylow or Cauchy)?

Published on 18 Feb 2019 - 13:17

score 107 · Answer 2 · 2026-03-12 06:40:45

107

Views

Why is $z = 1 + 1 + \dots + 1$ for all positive $z \in \mathbb{Z}$

Published on 12 Mar 2026 - 6:40

score 464 · Answer 3 · 2019-02-19 14:08:17

464

Views

A more natural solution to finding the general terms of a recurrence relation in $2$ variables

Published on 19 Feb 2019 - 14:08

score 199 · Answer 4 · 2026-03-25 17:42:07

199

Views

If $q^k n^2$ is an odd perfect number with special prime $q$, then $n^2 - q^k$ is not a square.

Published on 25 Mar 2026 - 17:42

score 91 · Answer 5 · 2026-03-27 17:52:35

91

Views

Finding out the remainder of $\frac{11^\text{10}-1}{100}$ using modulus

Published on 27 Mar 2026 - 17:52

score 189 · Answer 6 · 2026-03-25 12:26:04

189

Views

Proof: A graph that does not contain any closed walks with odd length is bipartite.

Published on 25 Mar 2026 - 12:26

score 1.5k · Answer 7 · 2019-02-25 20:34:11

1.5k

Views

Prove that $2018^{2019}> 2019^{2018}$ without induction, without Newton's binomial formula and without Calculus.

Published on 25 Feb 2019 - 20:34

score 38 · Answer 8 · 2026-03-25 12:21:16

38

Views

What is $\sigma(q^k)$ in terms of $k$ if $q \equiv 5 \pmod 8$?

Published on 25 Mar 2026 - 12:21

score 696 · Answer 9 · 2019-03-01 18:17:53

696

Views

Proof of exponential law using limit definition of exponential function?

Published on 01 Mar 2019 - 18:17

score 244 · Answer 10 · 2026-03-27 17:04:25

244

Views

Elements and cyclic subgroups of order $15$ in $\Bbb Z_{30}\times \Bbb Z_{20}.$

Published on 27 Mar 2026 - 17:04

score 125 · Answer 11 · 2019-03-08 15:54:30

125

Views

Prove $(\lnot p \to p) \to p$ in 19 steps

Published on 08 Mar 2019 - 15:54

score 179 · Answer 12 · 2019-03-10 23:03:57

179

Views

Picture proof that the area of a right triangle is $xy$

Published on 10 Mar 2019 - 23:03

score 392 · Answer 13 · 2019-03-11 10:34:54

392

Views

How did I solve this (triply logarithmic) equation?

Published on 11 Mar 2019 - 10:34

score 364 · Answer 14 · 2019-03-11 12:30:58

364

Views

Showing every connected regular space having more than one point is uncountable without using proof by contradiction

Published on 11 Mar 2019 - 12:30

score 129 · Answer 15 · 2019-03-11 18:59:31

129

Views

Show $\phi(n)$ = $n \Pi_{p \vert n} (1 - \frac{1}{p})$

Published on 11 Mar 2019 - 18:59

List Question

For distinct primes $p$ and $q$, does any group of order $p^2q$ have a subgroup of order $p$ (without using Sylow or Cauchy)?

Why is $z = 1 + 1 + \dots + 1$ for all positive $z \in \mathbb{Z}$

A more natural solution to finding the general terms of a recurrence relation in $2$ variables

If $q^k n^2$ is an odd perfect number with special prime $q$, then $n^2 - q^k$ is not a square.

Finding out the remainder of $\frac{11^\text{10}-1}{100}$ using modulus

Proof: A graph that does not contain any closed walks with odd length is bipartite.

Prove that $2018^{2019}> 2019^{2018}$ without induction, without Newton's binomial formula and without Calculus.

What is $\sigma(q^k)$ in terms of $k$ if $q \equiv 5 \pmod 8$?

Proof of exponential law using limit definition of exponential function?

Elements and cyclic subgroups of order $15$ in $\Bbb Z_{30}\times \Bbb Z_{20}.$

Prove $(\lnot p \to p) \to p$ in 19 steps

Picture proof that the area of a right triangle is $xy$

How did I solve this (triply logarithmic) equation?

Showing every connected regular space having more than one point is uncountable without using proof by contradiction

Show $\phi(n)$ = $n \Pi_{p \vert n} (1 - \frac{1}{p})$

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