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Anton Grudkin
  • Member for 6 years, 2 months
  • Last seen more than a week ago
827 votes
27 answers
195k views

How to study math to really understand it and have a healthy lifestyle with free time? [closed]

  • 10.2k
129 votes
20 answers
89k views

Real life applications of Topology

  • 2,879
114 votes
5 answers
10k views

A multiplication algorithm found in a book by Paul Erdős: how does it work?

  • 8,673
113 votes
11 answers
25k views

Am I just not smart enough? [closed]

  • 2,396
85 votes
7 answers
10k views

If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$

77 votes
7 answers
7k views

Does associativity imply commutativity?

  • 3,353
73 votes
15 answers
19k views

Solving $DEF+FEF=GHH$, $KLM+KLM=NKL$, $ABC+ABC+ABC=BBB$

  • 4,612
58 votes
10 answers
6k views

Is it an abuse of language to say "*the* integers," "*the* rational numbers," or "*the* real numbers," etc.?

  • 4,501
44 votes
6 answers
2k views

How many resistors are needed?

  • 1,248
40 votes
1 answer
1k views

Closed form for $\left(1+\left(\frac{1}{2}+\left(\frac{1}{3}+\left(\frac{1}{4}+\cdots\right)^2\right)^2\right)^2\right)^2$?

  • 30.4k
29 votes
1 answer
1k views

Prove that $\sqrt{a^2+3b^2}+\sqrt{b^2+3c^2}+\sqrt{c^2+3a^2}\geq6$ if $(a+b+c)^2(a^2+b^2+c^2)=27$

26 votes
5 answers
2k views

If $a^3+a^2+a=9b^3+b^2+b$ and $a,b$ are integers then show $a-b$ is a perfect cube.

  • 3,507
24 votes
3 answers
5k views

$AB=BA$ implies $AB^T=B^TA$ when $A$ is normal

23 votes
5 answers
1k views

If $a+b+c=abc$ then $\sum\limits_{cyc}\frac{1}{7a+b}\leq\frac{\sqrt3}{8}$

22 votes
2 answers
436 views

Prove that $\sum\limits_{cyc}\frac{a}{\sqrt{a+3b}}\geq\sqrt{a+b+c+d}$

20 votes
13 answers
5k views

What are examples of vectors that are not usually called vectors?

  • 5,125
20 votes
4 answers
2k views

Evaluate $\frac{0!}{4!}+\frac{1!}{5!}+\frac{2!}{6!}+\frac{3!}{7!}+\frac{4!}{8!}+\cdots$

  • 3,507
18 votes
3 answers
4k views

Additive function $T: \mathbb{R} \rightarrow \mathbb{R}$ that is not linear.

  • 3,226
18 votes
1 answer
772 views

Geometric inequality $\frac{R_a}{2a+b}+\frac{R_b}{2b+c}+\frac{R_c}{2c+a}\geq\frac{1}{\sqrt3}$

17 votes
5 answers
680 views

Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$

  • 769
15 votes
2 answers
832 views

Inequality with Sum of Binomial Coefficients

  • 7,903
14 votes
5 answers
1k views

Fastest way showing the limit exists without finding the limit?

  • 5,047
14 votes
1 answer
385 views

Prove $ \sin x + \frac{ \sin3x }{3} + ... + \frac{ \sin((2n-1)x) }{2n-1} >0 $

  • 1,938
14 votes
0 answers
307 views

Number as the sum of digits of some degree

13 votes
5 answers
2k views

Is $1 = [1] = [[1]] = [[[ 1 ]]], \ldots$?

  • 1,085
13 votes
2 answers
204 views

Proof that ${2x\over 2x-1}={A(x)\over A(x-1)}$ for every integer $x\ge2$, where $A(x)=\sum\limits_{n=0}^\infty\prod\limits_{k=0}^n\frac{x-k}{x+k}$

13 votes
2 answers
3k views

$AB-BA$ is a nilpotent matrix if it commutes with $A$

  • 38.1k
11 votes
4 answers
670 views

Prove that between any two rational numbers there is a rational whose numerator and denominator are both perfect squares.

  • 704
11 votes
2 answers
449 views

Determine all functions $f$ on $\mathbb R$ such that $f(x^2+yf(x))=f(x)f(x+y)$ for all $x,y$

  • 341
11 votes
2 answers
1k views

$\mathrm{rank}(AB-BA)=1$ implies $A$ and $B$ are simultaneously triangularisable

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