User Calvin Lin - Mathematics Stack Exchange

77 votes

Is there any branch of Mathematics which has no applications in any other field or in real world?

answered Jan 26, 2013 at 22:40

66 votes

Accepted

Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer

answered Feb 8, 2013 at 19:30

45 votes

Why can't you square both sides of an equation?

answered Nov 16, 2013 at 1:13

41 votes

Collection of surprising identities and equations.

answered Sep 26, 2013 at 0:50

41 votes

Accepted

prove $\sqrt{a_n b_n}$ and $\frac{1}{2}(a_n+b_n)$ have same limit

answered Dec 30, 2012 at 7:07

34 votes

Accepted

Is the number $0.112358132134...$ rational or irrational?

answered Sep 25, 2013 at 17:59

32 votes

Accepted

Prove that: $\sqrt{2\sqrt{3\sqrt{4\cdots\sqrt{n}}}}<3,\,\forall n\in\mathbb N.$

answered Aug 21, 2013 at 22:00

31 votes

Collection of surprising identities and equations.

answered Sep 26, 2013 at 0:52

31 votes

Accepted

Calculate $\underset{x\rightarrow7}{\lim}\frac{\sqrt{x+2}-\sqrt[3]{x+20}}{\sqrt[4]{x+9}-2}$

answered Jan 11, 2013 at 20:37

26 votes

Accepted

Prove that $5$ is the only prime $p$ such that $3p + 1$ is a perfect square

answered Aug 15, 2013 at 6:19

26 votes

What is the pattern to this sequence?

answered Sep 2, 2013 at 8:18

24 votes

Accepted

finding the remainder of $x^{100}-2x^{51}+1$

answered Apr 18, 2013 at 22:55

23 votes

Accepted

$n^5-n$ is divisible by $10$?

answered May 27, 2013 at 19:52

21 votes

Examples of patterns that eventually fail

answered Sep 22, 2013 at 21:27

20 votes

Accepted

When is $2^n \pm 1$ a perfect power

answered Sep 22, 2013 at 19:21

20 votes

Accepted

Puzzles or short exercises illustrating mathematical problem solving to freshman students

answered Sep 22, 2013 at 15:43

19 votes

Accepted

An amazing integral with a typo

answered Jun 16, 2023 at 0:19

18 votes

Prove that $\frac{100!}{50!\cdot2^{50}} \in \Bbb{Z}$

answered Jul 7, 2013 at 15:04

17 votes

Accepted

Solutions for x!/y!=(y+1)!

answered Aug 30, 2013 at 15:42

16 votes

Polynomials Question: Proving $a=b=c$.

answered Jun 25, 2013 at 18:18

16 votes

Accepted

Demonstration using the Pigonhole principle

answered May 15, 2013 at 5:42

16 votes

Perron-Frobenius theorem

answered Jan 2, 2013 at 0:27

15 votes

How to compute the determinant of a tridiagonal Toeplitz matrix?

answered Dec 29, 2012 at 11:55

15 votes

Accepted

Counting number of solutions with restrictions

answered May 28, 2013 at 19:36

15 votes

How to prove that $\lim\limits_{x\to0}\frac{\tan x}x=1$?

answered Jul 20, 2013 at 18:02

15 votes

Accepted

Integers $n$ for which $|2^n + 5^n – 65|$ is a perfect square

answered Jan 19, 2021 at 14:34

14 votes

Accepted

Show $\lim\limits_{n\to\infty} \sqrt[n]{n^e+e^n}=e$

answered Dec 29, 2012 at 11:13

14 votes

How can I prove that $xy\leq x^2+y^2$?

answered Apr 10, 2013 at 16:27

14 votes

On the "funny" identity $\tfrac{1}{\sin(2\pi/7)} + \tfrac{1}{\sin(3\pi/7)} = \tfrac{1}{\sin(\pi/7)}$

answered Sep 28, 2013 at 3:43

14 votes

Accepted

Prove that $2^n\alpha-[2^n\alpha]$ is dense in [0,1]

answered Dec 16, 2013 at 6:08

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2,162 Answers

Is there any branch of Mathematics which has no applications in any other field or in real world?

Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer

Why can't you square both sides of an equation?

Collection of surprising identities and equations.

prove $\sqrt{a_n b_n}$ and $\frac{1}{2}(a_n+b_n)$ have same limit

Is the number $0.112358132134...$ rational or irrational?

Prove that: $\sqrt{2\sqrt{3\sqrt{4\cdots\sqrt{n}}}}<3,\,\forall n\in\mathbb N.$

Collection of surprising identities and equations.

Calculate $\underset{x\rightarrow7}{\lim}\frac{\sqrt{x+2}-\sqrt[3]{x+20}}{\sqrt[4]{x+9}-2}$

Prove that $5$ is the only prime $p$ such that $3p + 1$ is a perfect square

What is the pattern to this sequence?

finding the remainder of $x^{100}-2x^{51}+1$

$n^5-n$ is divisible by $10$?

Examples of patterns that eventually fail

When is $2^n \pm 1$ a perfect power

Puzzles or short exercises illustrating mathematical problem solving to freshman students

An amazing integral with a typo

Prove that $\frac{100!}{50!\cdot2^{50}} \in \Bbb{Z}$

Solutions for x!/y!=(y+1)!

Polynomials Question: Proving $a=b=c$.

Demonstration using the Pigonhole principle

Perron-Frobenius theorem

How to compute the determinant of a tridiagonal Toeplitz matrix?

Counting number of solutions with restrictions

How to prove that $\lim\limits_{x\to0}\frac{\tan x}x=1$?

Integers $n$ for which $|2^n + 5^n – 65|$ is a perfect square

Show $\lim\limits_{n\to\infty} \sqrt[n]{n^e+e^n}=e$

How can I prove that $xy\leq x^2+y^2$?

On the "funny" identity $\tfrac{1}{\sin(2\pi/7)} + \tfrac{1}{\sin(3\pi/7)} = \tfrac{1}{\sin(\pi/7)}$

Prove that $2^n\alpha-[2^n\alpha]$ is dense in [0,1]