User Stefan4024

71 votes

Is $0! = 1$ because there is only one way to do nothing?

answered Jul 1, 2016 at 20:52

25 votes

Show that from a group of seven people whose (integer) ages add up to 332 one can select three people with the total age at least 142.

answered Aug 27, 2015 at 10:51

21 votes

Is there a way to get trig functions without a calculator?

answered Sep 22, 2013 at 20:56

17 votes

Accepted

Is every finite group a normal subgroup of a symmetric group?

answered Jun 27, 2016 at 23:14

15 votes

Accepted

Objects are shuffled. What is the probability that exactly one object remains in its original position?

answered Jan 24, 2017 at 20:24

15 votes

Proving that the polynomial $10X^6-15X^2+7$ is irreducible in $\mathbb{Q}[X].$

answered Jul 2, 2018 at 19:48

14 votes

Accepted

Equality of triangle inequality in complex numbers

answered Jan 26, 2014 at 19:19

13 votes

Showing the complex conjugate of an eigenvector to a given eigenvalue is an eigenvector for the conjugate eigenvalue.

answered Nov 16, 2017 at 11:04

12 votes

Accepted

Is $ \sqrt{2}$ an element of $ \mathbb{Q} ( \cos 72^\circ ) $?

answered Aug 9, 2018 at 2:03

12 votes

Prove that $\left(\frac12(x+y)\right)^2 \le \frac12(x^2 + y^2)$

answered Feb 5, 2014 at 21:46

12 votes

Accepted

Undergraduate mathematics competitions

answered Aug 16, 2015 at 17:16

11 votes

Accepted

How to put brackets into $10^2÷10÷10÷10÷10 = 10$ to make it correct?

answered Oct 7, 2016 at 16:09

11 votes

Accepted

Calculating this class number

answered Jun 18, 2018 at 23:22

11 votes

Evaluate: $\lim_{\theta \to \frac {\pi}{4}} \dfrac {\cos \theta - \sin \theta}{\theta - \frac {\pi}{4}}$

answered Jul 19, 2017 at 2:14

11 votes

Accepted

How can I show that the polynomial $p = x^5 - x^3 - 2x^2 - 2x - 1$ is irreducible over $\Bbb Q$?

answered Apr 9, 2017 at 11:21

10 votes

Find: $\lim_{x\to\infty} \frac{\sqrt{x}}{\sqrt{x+\sqrt{x+\sqrt{x}}}}.$

answered Dec 26, 2017 at 20:29

10 votes

How to show that $2730\mid n^{13}-n\;\;\forall n\in\mathbb{N}$

answered Dec 6, 2013 at 21:15

10 votes

Accepted

Find point on line that has integer coordinates

answered Sep 18, 2013 at 9:21

9 votes

Accepted

Derivative of a summation in order to minimize

answered Sep 14, 2013 at 2:31

9 votes

How to find $\lim_{x \to \frac{\pi}{6}}\frac{\sin(x)-\frac{1}{2}}{x-\frac{\pi}{6}}$ without using L'Hospital's Rule?

answered Sep 13, 2016 at 0:20

9 votes

How to find the closed formula for $\sum _{i=0}^n {i q^i}$?

answered Sep 19, 2016 at 15:54

9 votes

Accepted

Even numbers of the form $\frac {n(n+1)}{2}$ and twin primes

answered Aug 23, 2018 at 9:30

8 votes

Accepted

Distance between two stations

answered Aug 17, 2018 at 16:01

8 votes

Why multiplying powers of prime factors of a number yields number of total divisors?

answered Aug 9, 2018 at 22:02

8 votes

Accepted

If $ A^3=A$ prove that $Ker\left(A-I\right)+Im\left(A-I\right)=V$

answered Jan 28, 2017 at 12:47

8 votes

Accepted

Prove by induction that $\left [ \left (3+\sqrt{5} \right )^{n} + \left (3-\sqrt{5} \right )^{n} \right ]$ is multiple of $2^{n}$

answered Oct 1, 2016 at 17:19

8 votes

Drawer contains 14 socks. If I randomly pull 2, what is the probability that I will get a matching pair?

answered Aug 30, 2013 at 1:48

8 votes

Accepted

how is the probability of event will be affected by its successive events ??

answered Sep 22, 2013 at 15:00

8 votes

Fibonacci numbers expressed as squares of lower Fibonacci numbers

answered Jan 25, 2014 at 23:49

7 votes

Induction proof on Fibonacci sequence: $F(n-1) \cdot F(n+1) - F(n)^2 = (-1)^n$

answered Oct 12, 2013 at 22:26

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1,205 Answers

Is $0! = 1$ because there is only one way to do nothing?

Show that from a group of seven people whose (integer) ages add up to 332 one can select three people with the total age at least 142.

Is there a way to get trig functions without a calculator?

Is every finite group a normal subgroup of a symmetric group?

Objects are shuffled. What is the probability that exactly one object remains in its original position?

Proving that the polynomial $10X^6-15X^2+7$ is irreducible in $\mathbb{Q}[X].$

Equality of triangle inequality in complex numbers

Showing the complex conjugate of an eigenvector to a given eigenvalue is an eigenvector for the conjugate eigenvalue.

Is $ \sqrt{2}$ an element of $ \mathbb{Q} ( \cos 72^\circ ) $?

Prove that $\left(\frac12(x+y)\right)^2 \le \frac12(x^2 + y^2)$

Undergraduate mathematics competitions

How to put brackets into $10^2÷10÷10÷10÷10 = 10$ to make it correct?

Calculating this class number

Evaluate: $\lim_{\theta \to \frac {\pi}{4}} \dfrac {\cos \theta - \sin \theta}{\theta - \frac {\pi}{4}}$

How can I show that the polynomial $p = x^5 - x^3 - 2x^2 - 2x - 1$ is irreducible over $\Bbb Q$?

Find: $\lim_{x\to\infty} \frac{\sqrt{x}}{\sqrt{x+\sqrt{x+\sqrt{x}}}}.$

How to show that $2730\mid n^{13}-n\;\;\forall n\in\mathbb{N}$

Find point on line that has integer coordinates

Derivative of a summation in order to minimize

How to find $\lim_{x \to \frac{\pi}{6}}\frac{\sin(x)-\frac{1}{2}}{x-\frac{\pi}{6}}$ without using L'Hospital's Rule?

How to find the closed formula for $\sum _{i=0}^n {i q^i}$?

Even numbers of the form $\frac {n(n+1)}{2}$ and twin primes

Distance between two stations

Why multiplying powers of prime factors of a number yields number of total divisors?

If $ A^3=A$ prove that $Ker\left(A-I\right)+Im\left(A-I\right)=V$

Prove by induction that $\left [ \left (3+\sqrt{5} \right )^{n} + \left (3-\sqrt{5} \right )^{n} \right ]$ is multiple of $2^{n}$

Drawer contains 14 socks. If I randomly pull 2, what is the probability that I will get a matching pair?

how is the probability of event will be affected by its successive events ??

Fibonacci numbers expressed as squares of lower Fibonacci numbers

Induction proof on Fibonacci sequence: $F(n-1) \cdot F(n+1) - F(n)^2 = (-1)^n$