user avatar
user avatar
user avatar
SMM
  • Member for 7 years, 4 months
  • Last seen more than 1 year ago
22 votes

In the figure, a quarter circle, a semicircle and a circle are mutually tangent inside a square of side length $2$. Find the radius of the circle.

10 votes
Accepted

Rudin Ex 2.2: Proving countability of algebraic numbers with a hint

8 votes

Galois group of $x^4 + 2$ over $\mathbb{Q}$

8 votes

Find angle UFO in the picture attached

7 votes
Accepted

Does there exist irreducible polynomials of each degree over arbitrary field?

7 votes
Accepted

Show some $\mathbb{X} \subseteq \mathbb{N}^+$ occurs as the finite spectrum of a sentence for this language.

7 votes
Accepted

Left action of a group on permutation representation

7 votes
Accepted

Through two given points on a circle, construct two parallel chords with a given sum.

6 votes
Accepted

Finding determinant of $n \times n$ matrix

6 votes
Accepted

Groups of order $360$ have a subgroup of order $10$

5 votes
Accepted

Equilateral triangles on the sides of a triangle

5 votes
Accepted

Parametrizing the square spiral

4 votes
Accepted

Sum of subsets is the whole set?

4 votes

Definability of subgraphs of random graphs

4 votes
Accepted

The number of divisors of $0$ in a finite ring

4 votes
Accepted

Show that a subgroup of order $N \in \mathbb{N}$ is isomorphic to $\mathbb{Z}/n\mathbb{Z} × \mathbb{Z}/nn'\mathbb{Z}$.

4 votes
Accepted

Prove -1 Transformation (A binomial identity):$\binom{-p}{q}=\binom{p+q-1}{q}(-1)^q$

4 votes
Accepted

Do injective homomorphisms preserve generating sets?

3 votes
Accepted

$f(Y),g(Y)\in K[Y]$ coprime $\Rightarrow f(Y)-g(Y)X$ irreducible in $K(X)[Y]$

3 votes
Accepted

Inverse of a unipotent matrix

3 votes

Galois extension of $\mathbb{Q}$ with Galois group $\mathbb{Z}/4\mathbb{Z}$ that contains $\mathbb{Q}(\sqrt{3})$?

3 votes
Accepted

Let $G$ be non-abelian simple and $p$ largest prime divisor of $|G|$. If $H<G$, then $|G:H|\geq p$.

3 votes
Accepted

Squares on the sides of a regular pentagon

3 votes
Accepted

For $H$ the orthocenter of $\triangle ABC$, prove $|AH|h_a+|BH|h_b+|CH|h_c=\frac12\left(a^2+b^2+c^2\right)$

3 votes

Find angle without trigonometry

3 votes
Accepted

The minimal size of generating set of quotient group

3 votes
Accepted

A maximal regular ideal of commutative ring is prime?

3 votes
Accepted

All real functions such that $(x+y)(f(x) - f(y)) = (x - y)f(x + y)$

3 votes

Subsets of $\mathbb Z/n\mathbb Z$ disjoint with some of its shifts

3 votes
Accepted

Is there a way to put 5 points on the surface of the sphere so that they are indistinguishable?

1
2 3 4 5