User AlanH - Mathematics Stack Exchange

bio	website	math.stackexchange.com/users/…
	location	Antarctica
	age	77
visits	member for	7 months
	seen	2 mins ago
stats	profile views	142

	787 reputation	bio	website	math.stackexchange.com/users/…	visits	member for	7 months
219 badges		location	Antarctica		seen	2 mins ago

5

17

votes

9

answers

625

views

Comparing $\sqrt{1001}+\sqrt{999}\ , \ 2\sqrt{1000}$

algebra-precalculus problem-solving

20h ago RecklessReckoner 1,269

1

4

votes

4

answers

145

views

Find all entire functions $f$ such that $f^{(n)}(z) = z$ for all $z$, $n$ being a given positive integer

complex-analysis

may 13 at 14:04 Community♦ 1

5

8

votes

2

answers

144

views

Compute the remainder when $67!$ is divided by $71$.

number-theory elementary-number-theory

may 12 at 21:09 icanc 318

2

10

votes

6

answers

637

views

Proving a binomial sum identity

combinatorics binomial-coefficients generating-functions

may 9 at 15:05 J. M. 38.9k

19

120

votes

4

answers

4

kviews

Can you answer my son's fourth-grade homework question: Which numbers are prime, have digits adding to ten and have a three in the tens place?

elementary-number-theory recreational-mathematics analytic-number-theory

may 8 at 4:56 Dale M 404

14

31

votes

5

answers

884

views

How to prove this identity $\pi=\sum\limits_{k=-\infty}^{\infty}\left(\frac{\sin(k)}{k}\right)^{2}\;$?

sequences-and-series trigonometry pi

may 7 at 15:34 robjohn♦ 59.2k

9

14

votes

5

answers

488

views

Evaluate: $\int_0^{\pi} \ln \left( \sin \theta \right) d\theta$

complex-analysis integral logarithms

may 5 at 22:04 Ma Ming 1,812

103

205

votes

33

answers

17

kviews

Do complex numbers really exist?

soft-question complex-numbers teaching philosophy

may 5 at 4:54 l19 115

34

46

votes

17

answers

4

kviews

Striking applications of integration by parts

calculus big-list

may 3 at 13:19 DepeHb 485

53

151

votes

13

answers

17

kviews

Unusual 5th grade problem, how to solve it

elementary-number-theory diophantine-equations

may 1 at 13:18 doraemonpaul 2,991

3

13

votes

3

answers

395

views

Solving a difficult recursion via generating functions

homework recurrence-relations power-series generating-functions

may 1 at 1:17 vonbrand 6,548

1

3

votes

1

answer

70

views

Contour Integration: $\int_0^\infty\frac{1}{x^a(1-x)}\,dx$ for $0<a<1$.

homework complex-analysis contour-integration

apr 26 at 5:54 Ron Gordon 26k

9

15

votes

2

answers

238

views

How to find the value of $\sin{\dfrac{\pi}{14}}+6\sin^2{\dfrac{\pi}{14}}-8\sin^4{\dfrac{\pi}{14}}$

trigonometry

apr 18 at 13:59 TMM 7,156

1

3

votes

2

answers

30

views

Find the domain of $y=\cos^{-1}\left(\dfrac{1-2|x|}{3}\right)+\log_{|x-1|}x$

functions

apr 9 at 3:36 exploringnet 2,255

2

5

votes

1

answer

131

views

How can I prove that $H$ is the only non-trivial proper normal subgroup of $G$?

group-theory finite-groups

apr 3 at 16:54 Community♦ 1

6

16

votes

3

answers

320

views

Finding all integer solutions of $5^x+7^y=2^z$

number-theory elementary-number-theory diophantine-equations contest-math

apr 3 at 7:31 Ivan Loh 6,508

3

8

votes

3

answers

105

views

Prove that $\lim \limits_{n \to \infty} n^2 \int_{0}^{\frac{1}{n}} x^{x+1} dx = \dfrac{1}{2} $

real-analysis integral limit

apr 3 at 6:08 Fixed Point 2,012

1

vote

1

answer

20

views

More Continuity True and False

real-analysis

apr 3 at 1:45 Peej Gerard 241

3

5

votes

2

answers

129

views

How to prove that for all $m,n\in\mathbb N$, $\ 56786730 \mid mn(m^{60}-n^{60})$?

homework elementary-number-theory modular-arithmetic divisibility

apr 2 at 19:10 Community♦ 1

11

32

votes

7

answers

1

kviews

Inequality: $(a^3+a+1)(b^3+b+1)(c^3+c+1) \leq 27$

inequality

apr 1 at 20:01 Iuli 3,090

1

4

votes

2

answers

109

views

Calculate:$\int \frac{px^{p+2q-1} - qx^{q-1}}{x^{2p+2q}+2x^{p+q}+1} dx $

integral integration

apr 1 at 7:42 Caran-d'Ache 1,015

3

6

votes

1

answer

59

views

Find the floor value of a finite continued surd

algebra-precalculus elementary-number-theory

mar 31 at 9:09 Ivan Loh 6,508

13

14

votes

5

answers

1

kviews

Math GRE Subject Exam

education advice

mar 31 at 6:19 yiyi 1,966

10

17

votes

3

answers

358

views

How much time is too much (to put into a single problem)?

soft-question advice

mar 29 at 18:43 Feanor 2,865

5

8

votes

4

answers

178

views

The minimum value of $a^2+b^2+c^2+\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}?$

inequality

mar 29 at 8:36 Inceptio 4,375

1

4

votes

4

answers

96

views

Proving $\gcd(n^2(n^2+1),2n+1)=\gcd(2n+1,5)$

number-theory elementary-number-theory

mar 28 at 23:35 Community♦ 1

5

10

votes

1

answer

171

views

Graph theory question

graph-theory

mar 26 at 14:46 Aline Parreau 251

181

160

votes

23

answers

10

kviews

Proofs that every mathematician should know?

soft-question big-list

mar 25 at 0:36 Glen O 3,074

2

7

votes

4

answers

214

views

finding the coefficient of $x^{14}$ in the expression: $\frac{5x^2-x^4}{(1-x)^3}$

homework combinatorics generating-functions

mar 24 at 7:39 AlanH 787

3

6

votes

1

answer

162

views

how to prove $\sum _{|k|\lt\sqrt m}\binom{2m}{m+k}\ge2^{2m-1}$

homework probability combinatorics contest-math

mar 22 at 22:13 user17762 75.9k

AlanH

82 Favorites