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Calvin Lin's user avatar
Calvin Lin's user avatar
Calvin Lin's user avatar
Calvin Lin
  • Member for 13 years, 4 months
  • Last seen more than 1 year ago
77 votes

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

67 votes
Accepted

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

49 votes

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

43 votes

Collection of surprising identities and equations.

43 votes
Accepted

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

38 votes
Accepted

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

33 votes
Accepted

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

32 votes
Accepted

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

32 votes
Accepted

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

31 votes

Collection of surprising identities and equations.

26 votes

What is the pattern to this sequence?

24 votes
Accepted

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

23 votes
Accepted

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

21 votes

Examples of patterns that eventually fail

21 votes
Accepted

Puzzles or short exercises illustrating mathematical problem solving to freshman students

21 votes
Accepted

Expected number of cards that are larger than both of their neighbors

20 votes
Accepted

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

20 votes
Accepted

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

20 votes

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

19 votes
Accepted

An amazing integral with a typo

17 votes
Accepted

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

17 votes

How to compute the determinant of a tridiagonal Toeplitz matrix?

17 votes

Perron-Frobenius theorem

16 votes
Accepted

Demonstration using the Pigonhole principle

16 votes

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

15 votes
Accepted

Counting number of solutions with restrictions

15 votes

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

15 votes

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

14 votes
Accepted

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

14 votes

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

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