Taha Akbari's user avatar
Taha Akbari's user avatar
Taha Akbari's user avatar
Taha Akbari
  • Member for 8 years
  • Last seen this week
  • Tabriz, East Azerbaijan, Iran
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.

20 votes
4 answers
2k views

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

17 votes
7 answers
6k views

Evaluate $\sqrt[2]{2} \cdot \sqrt[4]{4}\cdot \sqrt[8]{8}\cdot \dots$

17 votes
1 answer
590 views

Do there exist four polynomials with real coefficients so that ...

13 votes
9 answers
683 views

Find all conditions for $x$ that the equation $1\pm 2 \pm 3 \pm 4 \pm \dots \pm n=x$ has a solution.

12 votes
5 answers
4k views

Create a monic polynomial with integer coefficients with $\sqrt[3]{2}+\sqrt[3]{3}+\sqrt[3]{5}$ as a root.

11 votes
2 answers
4k views

In how many ways can you colorize the vertices of a grid with 4 colors so that every unit-square vertices are all of a different color?

11 votes
4 answers
528 views

Place the numbers by their size.

11 votes
5 answers
2k views

How to calculate $3^{\sqrt{2}}$ with a simple calculator?

9 votes
6 answers
3k views

In how many $4$-digit numbers the sum of two right digits is equal to the sum of two left digits

8 votes
4 answers
213 views

Find $x$ and $y$ where $20!=\overline{24329020081766xy\dots}$

8 votes
4 answers
411 views

Find all the solutions of this equation:$x+3y=4y^3 \ , y+3z=4z^3\ , z+3x=4x^3 $ in reals.

8 votes
2 answers
1k views

Super hard complex numbers problem: there do not exist $n>1$ complex numbers $z_1, z_2, \ldots, z_n$, no two equal, such that for all $1 \le k \le n$

7 votes
3 answers
380 views

Prove using combinatorics $n \mid \binom{n}{m} \binom{n}{m-1}$

7 votes
2 answers
200 views

How many ways are there to train the players?

7 votes
3 answers
751 views

Why do $x^{x^{x^{\dots}}}=2$ and $x^{x^{x^{\dots}}}=4$ have the same positive root $\sqrt 2$?

6 votes
2 answers
642 views

Evaluate $\prod_{i=1}^{89} \sin (i)$ [duplicate]

6 votes
4 answers
624 views

Evaluate $\frac{1}{zx+y-1}+\frac{1}{zy+x-1}+\frac{1}{xy+z-1}$ if $x+y+z=2,x^2+y^2+z^2=3,xyz=4$

6 votes
1 answer
2k views

Prove that $\frac{1}{15}<\frac{1}{2}*\frac{3}{4}* \dots *\frac{99}{100}<\frac{1}{10}$ [duplicate]

6 votes
3 answers
708 views

Prove that $MN$ is parallel to $KL$.

5 votes
2 answers
211 views

Prove using combinatorics $\sum\limits_{r=0}^n2^{n-r}*\binom{n+r}{n}=2^{2n}$

5 votes
2 answers
209 views

count the number of words with length $n$ using $a,b,c$ that contain odd number of $a$'s.

5 votes
2 answers
729 views

Product of invertibles in $\Bbb Z_n$ [Wilson's Theorem generalization]

5 votes
4 answers
1k views

How many ways are there to color $1\times1$ squares in a $4\times5$ rectangle?

5 votes
2 answers
473 views

Find the minimum number of steps that we can arrange coins according to their weight

5 votes
4 answers
245 views

Factorize $x^4+16x-12$ over reals

5 votes
4 answers
393 views

Find $x^2+y^2+z^2$ if $x+y+z=0$ and $\sin{x}+\sin{y}+\sin{z}=0$ and $\cos{x}+\cos{y}+\cos{z}=0$ for any $x,y,z \in [-\pi,\pi]$

5 votes
2 answers
223 views

Find $b$ when $(2+\sqrt{3})^n=5042+b\sqrt{3}$

5 votes
1 answer
986 views

Cutting an equilateral triangle into $n$ equal pieces

4 votes
3 answers
212 views

numbers from $1$ to $2046$

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