User SMM

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.

answered May 6, 2019 at 12:15

11 votes

Accepted

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

answered Jan 30, 2015 at 22:43

8 votes

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

answered Feb 11, 2015 at 19:35

8 votes

Find angle UFO in the picture attached

answered Sep 5, 2018 at 7:42

7 votes

Accepted

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

answered Sep 1, 2018 at 19:27

7 votes

Accepted

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

answered Feb 1, 2015 at 21:32

7 votes

Accepted

Left action of a group on permutation representation

answered Apr 15, 2019 at 11:29

7 votes

Accepted

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

answered Jul 19, 2020 at 7:53

6 votes

Accepted

Parametrizing the square spiral

answered Mar 22, 2019 at 12:20

6 votes

Accepted

Finding determinant of $n \times n$ matrix

answered Jan 14, 2015 at 21:37

6 votes

Accepted

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

answered Sep 9, 2018 at 19:35

5 votes

Accepted

Equilateral triangles on the sides of a triangle

answered May 18, 2019 at 10:44

4 votes

Accepted

Sum of subsets is the whole set?

answered May 19, 2019 at 10:58

4 votes

Definability of subgraphs of random graphs

answered Apr 14, 2019 at 18:38

4 votes

Accepted

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

answered Sep 9, 2018 at 9:33

4 votes

Accepted

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

answered Nov 2, 2018 at 21:26

4 votes

Accepted

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

answered Sep 16, 2018 at 7:18

4 votes

Accepted

Do injective homomorphisms preserve generating sets?

answered Apr 28, 2018 at 17:46

3 votes

Accepted

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

answered Jan 14, 2015 at 14:57

3 votes

Accepted

Inverse of a unipotent matrix

answered Jan 17, 2015 at 19:14

3 votes

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

answered Jan 18, 2015 at 17:09

3 votes

Accepted

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

answered Sep 16, 2018 at 14:56

3 votes

Accepted

Squares on the sides of a regular pentagon

answered Feb 12, 2019 at 10:51

3 votes

Accepted

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

answered Nov 29, 2018 at 22:35

3 votes

Find angle without trigonometry

answered Nov 30, 2018 at 19:02

3 votes

Accepted

The minimal size of generating set of quotient group

answered Sep 9, 2018 at 14:31

3 votes

Accepted

A maximal regular ideal of commutative ring is prime?

answered Sep 11, 2018 at 22:06

3 votes

Accepted

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

answered Sep 12, 2018 at 14:14

3 votes

Accepted

Solving perpendicularity problem not using scalar product of vector

answered Apr 4, 2019 at 12:58

3 votes

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

answered Feb 14, 2019 at 10:12

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125 Answers

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.

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

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

Find angle UFO in the picture attached

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

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

Left action of a group on permutation representation

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

Parametrizing the square spiral

Finding determinant of $n \times n$ matrix

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

Equilateral triangles on the sides of a triangle

Sum of subsets is the whole set?

Definability of subgraphs of random graphs

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

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

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

Do injective homomorphisms preserve generating sets?

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

Inverse of a unipotent matrix

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

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

Squares on the sides of a regular pentagon

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

Find angle without trigonometry

The minimal size of generating set of quotient group

A maximal regular ideal of commutative ring is prime?

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

Solving perpendicularity problem not using scalar product of vector

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