User ᴊ ᴀ s ᴏ ɴ - Mathematics Stack Exchange

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	3,293 reputation	bio	website		visits	member for	1 year, 3 months
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8

18

votes

4

answers

1

kviews

Seems that I just proved $2=4$.

fake-proofs paradox

may 12 at 9:25 Martin Sleziak 20.8k

3

16

votes

3

answers

429

views

Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer.

number-theory

may 18 at 14:24 Inceptio 5,361

6

13

votes

2

answers

208

views

Show that $\frac 1 {\sqrt{x+y}}+\frac 1 {\sqrt{y+z}}+\frac 1 {\sqrt{z+x}}\geq2+\frac 1 {\sqrt2}$.

inequality

9h ago Shuhao Cao 7,696

4

13

votes

5

answers

799

views

Show that $\sqrt[3]{2+\frac {10} 9\sqrt 3}+\sqrt[3]{2-\frac {10} 9\sqrt 3}=2$

roots

may 12 at 13:07 ᴊ ᴀ s ᴏ ɴ 3,293

13

votes

11

answers

1

kviews

If $f(x)\leq f(f(x))$ for all $x$, is $x\leq f(x)$?

functions functional-inequalities

apr 2 at 0:21 Community♦ 1

1

11

votes

7

answers

641

views

Does $\,x>0\,$ hint that $\,x\in\mathbb R\,$?

real-analysis notation

may 20 at 3:50 bubba 4,957

1

11

votes

2

answers

102

views

Find the minimum of $q$.

elementary-number-theory

may 18 at 22:42 Goos 2,234

2

11

votes

4

answers

489

views

Solve $\cos^{n}x-\sin^{n}x=1$ with $n\in \mathbb{N}$.

algebra-precalculus trigonometry

aug 9 at 4:58 lab bhattacharjee 32.7k

2

10

votes

5

answers

287

views

Why don't we include $\pm\infty$ in $\mathbb R$?

analysis

jun 9 at 20:24 Rolazaro Azeveires 316

3

9

votes

0

answers

77

views

Solve $x^x=2x$ where $x\in\mathbb C$.

algebra-precalculus

1d ago ᴊ ᴀ s ᴏ ɴ 3,293

4

9

votes

3

answers

764

views

Evaluate $\int \cos(\cos x) dx$

calculus integral integration

may 15 at 14:17 ᴊ ᴀ s ᴏ ɴ 3,293

1

8

votes

1

answer

119

views

Is $10^n+1$ composite for all $n\in \mathbb{N}$ greater then $2$?

number-theory

dec 15 at 8:03 Isomorphism 1,578

2

8

votes

5

answers

261

views

Evaluate $\sum_{k=1}^\infty \frac{k^2}{(k-1)!}$.

calculus sequences-and-series

oct 27 at 14:26 Chris's wise sister 11.6k

3

8

votes

2

answers

152

views

Solve $x^{y^2}=y^x$ which $x,y\in\mathbb{N}$.

number-theory diophantine-equations

oct 17 at 15:02 mercio 12.1k

7

votes

3

answers

205

views

Proving there are no integers $a, b, c$ satisfying $12a + 18b + 27c = 227$

elementary-number-theory diophantine-equations

mar 30 at 16:55 Community♦ 1

1

7

votes

3

answers

142

views

Prove that $ \left(1+\frac a b \right) \left(1+\frac b c \right)\left(1+\frac c a \right) \geq 2\left(1+ \frac{a+b+c}{\sqrt[3]{abc}}\right)$.

inequality

feb 25 at 5:40 Loronegro 217

3

7

votes

5

answers

322

views

Are there any ways to evaluate $\int^\infty_0\frac{\sin x}{x}dx$ without using double integral?

integral integration definite-integral

jan 19 at 23:13 Mårten W 913

1

7

votes

1

answer

104

views

Find the smallest possible value of $a_1$.

sequences-and-series

dec 15 at 6:54 ᴊ ᴀ s ᴏ ɴ 3,293

1

7

votes

4

answers

868

views

Solve $(\sqrt{5+2\sqrt{6}})^{x}+(\sqrt{5-2\sqrt{6}})^{x}=10$.

algebra-precalculus

sep 27 at 9:06 Avatar 8,525

3

7

votes

2

answers

893

views

Strategies to denest nested radicals.

algebra-precalculus

sep 15 at 15:35 Community♦ 1

2

6

votes

4

answers

185

views

Find $f:\mathbb R\to\mathbb R$ such that $f(x)=f'(x)$.

calculus derivatives

apr 17 at 20:48 Seirios 9,800

3

6

votes

2

answers

120

views

Evaluating $\frac 9 {10}\cdot\frac {99} {100}\cdot\frac {999} {1000}\cdots$ [duplicate]

sequences-and-series

apr 13 at 13:31 Ben Norris 111

5

6

votes

1

answer

128

views

Prove that every element of $a_{n+2013}=\frac{a_{n+1}a_{n+2}…a_{n+2012}+1}{a_n}$ is an integer

sequences-and-series recurrence-relations

mar 26 at 16:16 Ivan Loh 8,098

6

votes

1

answer

114

views

Prove that for all non-negative integers $m,n$, $\frac{(2m)!(2n)!}{m!n!(m + n)!}$ is an integer.

number-theory

oct 17 at 4:48 user17762 78.6k

2

6

votes

6

answers

251

views

Solve $5a^2 - 4ab - b^2 + 9 = 0$, $ - 21a^2 - 10ab + 40a - b^2 + 8b - 12 = 0$

homework algebra-precalculus quadratics

oct 11 at 6:06 Martin Sleziak 20.8k

1

6

votes

3

answers

388

views

Simplify $\sqrt {\sqrt[3]{5}-\sqrt[3]{4}}$.

algebra-precalculus

sep 11 at 14:18 MJD 22.1k

5

votes

2

answers

70

views

Show $\sum_{a_1=1}^n\sum_{a_2=1}^{a_1}\sum_{a_3=1}^{a_2}…\sum_{a_m=1}^{a_{m-1}}a_m=\frac 1 {(m+1)!}\prod_{k=0}^m(n+k)$.

sequences-and-series

mar 3 at 14:27 Yimin 1,521

1

5

votes

2

answers

196

views

Method to find $\sin (2\pi/7)$

trigonometry

feb 23 at 8:15 lab bhattacharjee 32.7k

5

votes

2

answers

176

views

Is there any way to judge if a triangle is acute or obtuse?

geometry

sep 24 at 12:11 DonAntonio 51.1k

5

votes

2

answers

182

views

An Interesting Question about Pythagorean Triples

geometry algebra-precalculus number-theory

aug 14 at 9:42 AakashM 289

ᴊ ᴀ s ᴏ ɴ

130 Questions