User Stefan4024

43 votes

5 answers

14k views

Fermat's Last Theorem near misses?

asked Oct 14, 2013 at 21:15

21 votes

4 answers

10k views

Prove $\sqrt{a} + \sqrt{b} + \sqrt{c} \ge ab + bc + ca$

asked Mar 20, 2013 at 23:09

19 votes

4 answers

897 views

Find the smallest k such that $n^k > \sum_{i=0}^{n-1} i^k$

asked Feb 21, 2014 at 1:40

18 votes

7 answers

8k views

Prove $\sqrt{3a + b^3} + \sqrt{3b + c^3} + \sqrt{3c + a^3} \ge 6$

asked Mar 20, 2013 at 23:21

13 votes

2 answers

1k views

Prove $\frac{1}{2a+2bc+1} + \frac{1}{2b+2ca+1} + \frac{1}{2c+2ab+1} \ge 1$

asked Apr 2, 2013 at 22:59

9 votes

2 answers

2k views

Solve $a^3 + b^3 + c^3 = 6abc$

asked Sep 25, 2013 at 0:21

9 votes

3 answers

14k views

How to solve polynomial-exponential equation

asked Sep 27, 2013 at 23:12

8 votes

1 answer

890 views

Prove $\frac {1}{\cos 0^\circ \cdot \cos 1^\circ} + \ldots +\frac {1}{\cos 88^\circ \cdot \cos 89^\circ}= \frac{\cos 1^\circ}{\sin 1^\circ}$

asked Sep 29, 2013 at 23:41

8 votes

1 answer

3k views

How to draw ellipse and circle tangent to each other?

asked Aug 11, 2013 at 0:16

8 votes

1 answer

245 views

Find all natural numbers such that $\sum_{k=1}^{n} \frac{n^k}{k!}$ is an integer

asked Apr 1, 2014 at 22:18

8 votes

2 answers

259 views

Sum of remainders of Triangular numbers

asked Aug 5, 2016 at 11:27

7 votes

1 answer

2k views

Solve the simultaneous equations $x + \frac{3x-y}{x^2+y^2} = 3 $, $ y – \frac{x+3y}{x^2+y^2} = 0$

asked Sep 17, 2013 at 0:54

6 votes

0 answers

230 views

Apple game question

asked Feb 23, 2014 at 21:06

6 votes

3 answers

406 views

Prove that: $\sqrt[3]{a_1^3+ a_2^3 +\cdots+a_n^3} \le \sqrt{a_1^2 + a_2^2 +\cdots+a_n^2}$ [duplicate]

asked Mar 5, 2015 at 22:35

6 votes

1 answer

144 views

$f(x) = k^n$ for infinitely many integers $k$

asked Mar 12, 2015 at 18:14

6 votes

2 answers

1k views

Game-winning strategy

asked Feb 29, 2016 at 9:38

5 votes

1 answer

421 views

Normal closure is minimal normal subgroup

asked Jul 22, 2017 at 12:46

5 votes

3 answers

2k views

Prove that $(a+1)(a+2)...(a+b)$ is divisible by $b!$ [duplicate]

asked May 9, 2013 at 22:54

4 votes

1 answer

2k views

Minimize the sum of distances between two point and a circle

asked Aug 10, 2013 at 0:46

4 votes

1 answer

2k views

Distances to line passing through the centroid of triangle

asked Jan 30, 2014 at 18:43

4 votes

1 answer

2k views

Solve $x+y+z = x^3 + y^3 + z^3 = 8$ in $\mathbb{Z}$

asked Aug 31, 2013 at 14:30

4 votes

5 answers

924 views

How to explain infinity to a $3^{rd}$ grader?

asked Sep 30, 2013 at 19:21

4 votes

3 answers

5k views

Prove that if one function is greater or equal than another, then so it is its limit.

asked Nov 7, 2015 at 17:35

3 votes

0 answers

60 views

$m+n = (n,m)^2; n+l = (n,l)^2; l+m = (m,l)^2$

asked Apr 2, 2015 at 17:05

3 votes

1 answer

61 views

Numbers of matrices satisfying certain property

asked Apr 19, 2016 at 19:58

3 votes

2 answers

3k views

Solve exponential-polynomial equation

asked Feb 13, 2014 at 23:12

3 votes

1 answer

801 views

Solve an inequality using Cauchy-Schwarz Inequality

asked Jan 23, 2015 at 20:14

3 votes

0 answers

55 views

Subgroup of a given index [duplicate]

asked Sep 8, 2017 at 23:16

3 votes

2 answers

217 views

Socks on a clothing line

asked Sep 30, 2017 at 15:13

3 votes

3 answers

839 views

Tensor is non-zero

asked Apr 29, 2019 at 16:37

Stack Exchange Network

58 Questions

Fermat's Last Theorem near misses?

Prove $\sqrt{a} + \sqrt{b} + \sqrt{c} \ge ab + bc + ca$

Find the smallest k such that $n^k > \sum_{i=0}^{n-1} i^k$

Prove $\sqrt{3a + b^3} + \sqrt{3b + c^3} + \sqrt{3c + a^3} \ge 6$

Prove $\frac{1}{2a+2bc+1} + \frac{1}{2b+2ca+1} + \frac{1}{2c+2ab+1} \ge 1$

Solve $a^3 + b^3 + c^3 = 6abc$

How to solve polynomial-exponential equation

Prove $\frac {1}{\cos 0^\circ \cdot \cos 1^\circ} + \ldots +\frac {1}{\cos 88^\circ \cdot \cos 89^\circ}= \frac{\cos 1^\circ}{\sin 1^\circ}$

How to draw ellipse and circle tangent to each other?

Find all natural numbers such that $\sum_{k=1}^{n} \frac{n^k}{k!}$ is an integer

Sum of remainders of Triangular numbers

Solve the simultaneous equations $x + \frac{3x-y}{x^2+y^2} = 3 $, $ y – \frac{x+3y}{x^2+y^2} = 0$

Apple game question

Prove that: $\sqrt[3]{a_1^3+ a_2^3 +\cdots+a_n^3} \le \sqrt{a_1^2 + a_2^2 +\cdots+a_n^2}$ [duplicate]

$f(x) = k^n$ for infinitely many integers $k$

Game-winning strategy

Normal closure is minimal normal subgroup

Prove that $(a+1)(a+2)...(a+b)$ is divisible by $b!$ [duplicate]

Minimize the sum of distances between two point and a circle

Distances to line passing through the centroid of triangle

Solve $x+y+z = x^3 + y^3 + z^3 = 8$ in $\mathbb{Z}$

How to explain infinity to a $3^{rd}$ grader?

Prove that if one function is greater or equal than another, then so it is its limit.

$m+n = (n,m)^2; n+l = (n,l)^2; l+m = (m,l)^2$

Numbers of matrices satisfying certain property

Solve exponential-polynomial equation

Solve an inequality using Cauchy-Schwarz Inequality

Subgroup of a given index [duplicate]

Socks on a clothing line

Tensor is non-zero