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Sergey Filkin's user avatar
Sergey Filkin's user avatar
Sergey Filkin's user avatar
Sergey Filkin
  • Member for 12 years, 8 months
  • Last seen more than a month ago
10 votes
1 answer
9k views

Number of solutions of $x^2=1$ in $\mathbb{Z}/n\mathbb{Z}$

10 votes
2 answers
7k views

Find irreducible but not prime element in $\mathbb{Z}[\sqrt{5}]$

10 votes
1 answer
2k views

Prove that $\mathbb{C}[x,y] \ncong \mathbb{C}[x]\oplus\mathbb{C}[y]$

9 votes
5 answers
2k views

Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$

7 votes
2 answers
3k views

Infinite quantity of primes of the form $4k+1$

6 votes
2 answers
2k views

List all subgroups of the symmetry group of $n$-gon

6 votes
2 answers
1k views

Power series that diverges in specified number of points on the circle of convergence

5 votes
1 answer
9k views

Prove that curve with zero torsion is planar

5 votes
3 answers
4k views

Find maximal number of subsets of the set $U$ such that no one is a subset of another

5 votes
1 answer
715 views

Symmetry group of the dodecahedron and its subsets

5 votes
5 answers
349 views

Generalize the equality $\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\cdots+\frac{1}{n\cdot(n+1)}=\frac{n}{n+1}$

4 votes
2 answers
1k views

Is it possible to sort an array of 10 elements with 20 comparisons of two elements?

3 votes
1 answer
2k views

Number of 3x3 matrices with determinant $1$ and coefficients in $\mathbb{Z}_5$

3 votes
1 answer
78 views

Expectation of discrete random variable $X$ with $\mathbb{P}[X=n]=\frac{C}{n(n+1)(n+2)}$

3 votes
1 answer
71 views

Prove $ |A \cup B| = |[0,1]| \Rightarrow |A|=|[0,1]| \bigvee |B|=|[0,1]| $

3 votes
1 answer
585 views

Represent $\mathbb{R}^3$ as an union of disjoint circles using stereographic projection

3 votes
1 answer
2k views

Another proof of $A \triangle (B \triangle C)=(A \triangle B) \triangle C$

3 votes
1 answer
857 views

When $K[x]$ is a field?

3 votes
1 answer
1k views

Prove that $\mathbb{R}[x]/(x^2) \not\simeq \mathbb{R}[x]/(x^2-1) \not\simeq \mathbb{R}[x]/(x^2+1)$

2 votes
3 answers
140 views

Count points and lines in $\mathbb{A}^2(\mathbb{F}_p)$

2 votes
1 answer
2k views

Find all ideals of $F[x]$ and $F[[x]]$.

2 votes
4 answers
5k views

Calculate $\int_{0}^{2\pi}{\sin^8x}\ {dx}$

2 votes
1 answer
120 views

Why is the image of $M\times N\rightarrow M\otimes N, (m,n)\mapsto m\otimes n$ not a submodule?

1 vote
0 answers
88 views

Prove that $Fun(X)\otimes_\Bbb{C}Fun(Y)\cong Fun(X\oplus Y)$

1 vote
2 answers
97 views

Calculate $\lim_{n \to \infty} \frac{1^4 + 3^4 + \ldots + (2n-1)^4}{n^5}$

1 vote
2 answers
553 views

Prove that partial sums of $\sum_{n=1}^{\infty}{z^n}, z \in \mathbb{C}, |z|=1$ are bounded

1 vote
2 answers
188 views

Prove that $A^{\oplus n} \otimes_A N \cong N^{\oplus n}$