Question

Let $ba=a^4b^3$, show that $\mathrm{ord}(a^4b)=\mathrm{ord}(a^2b^3)$

score 64 · Answer 1 · 2026-04-01 20:36:42

64

Views

Let $ba=a^4b^3$, show that $\mathrm{ord}(a^4b)=\mathrm{ord}(a^2b^3)$

Published on 01 Apr 2026 - 20:36

score 280 · Answer 2 · 2026-03-29 18:53:37

280

Views

In a $n \times n$ grid of points, choosing $2n-1$ points, there will always be a right triangle

Published on 29 Mar 2026 - 18:53

score 49 · Answer 3 · 2026-04-01 20:38:09

49

Views

Bound on the size of a subset of a group give that there's an element $a$ such that $(xa)^3=1$ for all $x \in H$ (subgroup)

Published on 01 Apr 2026 - 20:38

score 150 · Answer 4 · 2020-06-13 20:48:20

150

Views

Sum of first K primes is triangle number

Published on 13 Jun 2020 - 20:48

score 1.6k · Answer 5 · 2026-04-01 22:20:46

1.6k

Views

Prove that there exists a positive integer $k$ such that $k2^n + 1$ is composite for every positive integer $n$.

Published on 01 Apr 2026 - 22:20

score 134 · Answer 6 · 2026-03-26 04:29:43

134

Views

An old APMO problem involving combinatorial geometry

Published on 26 Mar 2026 - 4:29

score 321 · Answer 7 · 2020-06-14 16:16:59

321

Views

Time rate problem involving trains don't know if my answer is correct

Published on 14 Jun 2020 - 16:16

score 277 · Answer 8 · 2026-03-25 10:57:17

277

Views

Number of times a pattern needs to be repeated on a Rubik's cube until it returns to solved

Published on 25 Mar 2026 - 10:57

score 89 · Answer 9 · 2026-03-30 14:41:14

89

Views

Show that $\binom{n}{1}-3\binom{n}{3}+3^2\binom{n}{5}\cdots=0$

Published on 30 Mar 2026 - 14:41

score 174 · Answer 10 · 2020-06-16 10:51:50

174

Views

How many distinct quadrilaterals can you draw inside a square of side length $4$?

Published on 16 Jun 2020 - 10:51

score 478 · Answer 11 · 2026-03-27 08:57:30

478

Views

Vic can beat Harold by $1/10$ of a mile in a $2$ mile race. Harold can beat Charlie by $1/5$ of a mile in a $2$ mile race. Very Confused.

Published on 27 Mar 2026 - 8:57

score 66 · Answer 12 · 2026-03-27 08:56:04

66

Views

How many fruit are there after a night on an alien planet

Published on 27 Mar 2026 - 8:56

score 518 · Answer 13 · 2026-03-29 13:21:18

518

Views

What does $[5.9]$ mean?

Published on 29 Mar 2026 - 13:21

score 110 · Answer 14 · 2026-04-01 22:19:03

110

Views

I have this identity that I'd like to prove. $\sum_{k=0}^{n}\left(\frac{n-2k}{n}\binom{n}{k}\right)^2=\frac{2}{n}\binom{2n-2}{n-1}$

Published on 01 Apr 2026 - 22:19

score 39 · Answer 15 · 2026-04-01 22:18:05

39

Views

Why does $\sum_{i=n}^{2n-1}\binom{i-1}{n-1}2^{1-i}$ computes the probability of $n$ head or tails

Published on 01 Apr 2026 - 22:18

List Question

Let $ba=a^4b^3$, show that $\mathrm{ord}(a^4b)=\mathrm{ord}(a^2b^3)$

In a $n \times n$ grid of points, choosing $2n-1$ points, there will always be a right triangle

Bound on the size of a subset of a group give that there's an element $a$ such that $(xa)^3=1$ for all $x \in H$ (subgroup)

Sum of first K primes is triangle number

Prove that there exists a positive integer $k$ such that $k2^n + 1$ is composite for every positive integer $n$.

An old APMO problem involving combinatorial geometry

Time rate problem involving trains don't know if my answer is correct

Number of times a pattern needs to be repeated on a Rubik's cube until it returns to solved

Show that $\binom{n}{1}-3\binom{n}{3}+3^2\binom{n}{5}\cdots=0$

How many distinct quadrilaterals can you draw inside a square of side length $4$?

Vic can beat Harold by $1/10$ of a mile in a $2$ mile race. Harold can beat Charlie by $1/5$ of a mile in a $2$ mile race. Very Confused.

How many fruit are there after a night on an alien planet

What does $[5.9]$ mean?

I have this identity that I'd like to prove. $\sum_{k=0}^{n}\left(\frac{n-2k}{n}\binom{n}{k}\right)^2=\frac{2}{n}\binom{2n-2}{n-1}$

Why does $\sum_{i=n}^{2n-1}\binom{i-1}{n-1}2^{1-i}$ computes the probability of $n$ head or tails

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