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SMM's user avatar
SMM
  • Member for 9 years, 5 months
  • Last seen this week
21 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.

12 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

Parametrizing the square spiral

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

4 votes
Accepted

Sum of subsets is the whole set?

4 votes

Volume of a tetrahedron with perpendicular opposite edges that are also perpendicular to the segment joining their midpoints

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

Set of conjugates of element cannot be contained in the union of two proper subgroups

3 votes
Accepted

Inverse of a unipotent matrix

3 votes
Accepted

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

3 votes

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

3 votes

A first order sentence such that the finite spectrum of that sentence is the following subsets of $\mathbb{N}^+$.

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?

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