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user2345215
  • Member for 10 years, 3 months
  • Last seen more than 7 years ago
70 votes

Factor $x^4+1$ over $\mathbb{R}$

34 votes
Accepted

A continuous function on $[0,1]$ not of bounded variation

33 votes

Prove that the closure of complement, is the complement of the interior

31 votes
Accepted

Is there a maximum value between open $(0,1)$ set?

25 votes
Accepted

Is the product of any two invertible diagonalizable matrices diagonalizable?

19 votes
Accepted

How to evaluate $\lim_{n\to\infty}\sqrt[n]{\frac{1\cdot3\cdot5\cdot\ldots\cdot(2n-1)}{2\cdot4\cdot6\cdot\ldots\cdot2n}}$

18 votes

which is bigger $2^{n^{1.001}}$ or $n!$

17 votes

Example of two open balls such that the one with the smaller radius contains the one with the larger radius.

16 votes
Accepted

Sum of digits raised to a power

15 votes
Accepted

$a^3+3a^2+a$ is never a perfect square.

13 votes
Accepted

Is every connected subset of the Sierpiński triangle arcwise connected?

12 votes

Show that $\int \limits_{0}^{\pi} f(\sin x) \cos x dx=0$ for any $f$ continuous on $[0,1]$

11 votes

Infinity Hotel problem

11 votes

Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law]

11 votes
Accepted

Proving the sum of squares of sine and cosine using the Cauchy product formula

11 votes
Accepted

How to prove $x^ax^b = x^{a+b}$

10 votes
Accepted

How to determine if a graph has a perfect matching?

10 votes

If $A^4=I$ then $A$ must be diagonalizable?

10 votes

Proof of $\sin^2(x) + \cos^2(x)=1$ using series

10 votes
Accepted

Can a function be shown positive without derivative?

10 votes
Accepted

Why $\Bbb Z$ = (integers) is an integral domain?

10 votes

How to solve this equation? $y^4-2y^2-\sqrt{y+1}=0$

9 votes
Accepted

Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.

8 votes

Other representations of factorial

8 votes
Accepted

Integrating $\int \frac{dx}{x^2+x+1}$

8 votes
Accepted

Why (cf)' = c(f)'

8 votes

Find remainder when $2^{30}\cdot 3^{20}$ is divided by $7$ without using calculator

8 votes
Accepted

Limit of logarithm function, $\lim\limits_{n\to\infty}\frac{n}{\log \left((n+1)!\right)}$

8 votes

How prove this sequence $S_{n}=[2^n\cdot \sqrt{2}],n\in N$ contains infinitely many composite numbers

8 votes
Accepted

Prove that positive $x,y$ satisfy $\left(\frac{1}{1+x}\right)^2+\left(\frac{1}{1+y}\right)^2\ge\frac{1}{1+xy}$.

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