User Oliver Kayende

5 votes

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If $\int\limits_0^1\frac{x^n}{1+x}\,\mathrm{d}x=\xi_n^n\,\ln 2,$ prove that $\xi_n^n \to 0$

answered Oct 25, 2019 at 1:42

4 votes

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Show that $\cos x=x^3+x^2+4x$ has exactly one root in $[0,\frac{\pi}{2}]$

answered Nov 12, 2019 at 4:24

4 votes

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Does the Frobenius endomorphism apply to polynomials?

answered Mar 1, 2020 at 19:44

3 votes

Group of units of a non-finitely generated ring

answered Nov 22, 2019 at 18:51

3 votes

Isomorphic subgroups such that the quotient is isomorphic.

answered Oct 9, 2019 at 21:58

3 votes

Finding a generator for a principal ideal

answered Oct 23, 2019 at 11:04

3 votes

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Let $G$ be a finite abelian group, and let $n$ divide $|G|$. Let $m$ be the number of solutions of $x^n=1$. Prove that $n\mid m$.

answered Nov 1, 2020 at 1:50

3 votes

Accepted

Why is $A \rtimes B \simeq \mathbb Z \rtimes \mathbb Z/2\mathbb Z$

answered Jan 31, 2021 at 16:41

3 votes

A prime ideal of $\mathbb{Z} \times \mathbb{Z}$ that is not maximal.

answered Feb 13, 2021 at 2:46

3 votes

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Showing that union over a collection of connected sets $\{F_n\}$ with $F_i\cap F_j \neq \varnothing, i\neq j$ is connected.

answered Jun 18, 2021 at 13:42

2 votes

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In search for easy counterexample of $L^2$ ineq. - if it exists

answered Jul 9, 2021 at 0:37

2 votes

Accepted

Prove that $F[x,y] / (y^2-x)$ is an integral domain

answered Feb 16, 2021 at 12:32

2 votes

Accepted

Is the order of a quotient of the multiplicative group of integers a prime power if the group is cyclic?

answered Feb 13, 2021 at 3:58

2 votes

When two elements of a group generate the same subgroup

answered Dec 31, 2020 at 10:52

2 votes

Finding points of discontinuity of $f(x)=\lim_{t\to\infty}\frac{|a+\sin(\pi x)|^t-1}{|a+\sin(\pi x)|^t+1}$

answered Jun 1, 2020 at 13:10

2 votes

Accepted

Let $G$ be a nonabelian group of order $p^{3},$ where $p$ is a prime. Show that $G$ has exactly $p^{2}+p-1$ distinct conjugacy classes.

answered Jun 5, 2020 at 13:04

2 votes

To Prove $ \bigcap_{i \in I} A_i \in \bigcap_{i \in I} P(A_i) $

answered Jun 20, 2020 at 16:12

2 votes

Accepted

Understanding the biconditional logical connective in the set: $K = \{x \in G: x \circ a \circ x^{-1} \in H \iff a \in H \}$

answered Oct 24, 2019 at 5:50

2 votes

In $\mathbb Z[x]$, find an ideal $P$ such that $R/P$ consists of $4$ elements.

answered Oct 14, 2019 at 21:57

2 votes

Evaluating $\int_{0}^{1}\int_{0}^{1}\sqrt{x^{2}+y^{2}}dxdy$ using polar coordinates.

answered Dec 14, 2019 at 8:48

2 votes

Show that $\langle x,y,z \rangle$ has order $42$ for $x,y,z$ with given properties

answered Dec 25, 2019 at 17:10

2 votes

The number of subgroups of $Z_{p^2}$ $\oplus$ $Z_{p^2}$ which are isomorphic to $Z_{p^2}$.

answered Mar 1, 2020 at 10:22

2 votes

If $n \geq 3$ then there is no surjective homomorphism $f: D_{2n} \to Z_n$.

answered Mar 20, 2020 at 5:46

2 votes

Accepted

Epimorphism from $\mathbb{Z}[i]$ to $\mathbb{F}_{p}$ where $p\equiv1 \pmod 4$

answered Feb 26, 2020 at 10:02

2 votes

Preimage of subgroup $H \subseteq G/N$ has order $|H| \cdot |N|$

answered Mar 17, 2020 at 23:27

2 votes

Why is it impossible for the mapping $x\mapsto 1/x$ to be a polynomial in an infinite field?

answered Apr 21, 2020 at 9:32

2 votes

Accepted

First isomorphism theorem $G=\mathbb{Z}/60\mathbb{Z}=<\overline{1}>$

answered May 16, 2020 at 10:24

1 vote

How can i find a solution of this optimization problem?

answered Apr 22, 2020 at 22:53

1 vote

Proving that $\bigcap \mathcal P\subseteq\left(\bigcap\mathcal M\right)\cup\left(\bigcup\mathcal N\right)$

answered Mar 18, 2020 at 9:39

1 vote

Accepted

Density of a countable union of rational lines

answered Feb 27, 2020 at 18:06

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135 Answers

If $\int\limits_0^1\frac{x^n}{1+x}\,\mathrm{d}x=\xi_n^n\,\ln 2,$ prove that $\xi_n^n \to 0$

Show that $\cos x=x^3+x^2+4x$ has exactly one root in $[0,\frac{\pi}{2}]$

Does the Frobenius endomorphism apply to polynomials?

Group of units of a non-finitely generated ring

Isomorphic subgroups such that the quotient is isomorphic.

Finding a generator for a principal ideal

Let $G$ be a finite abelian group, and let $n$ divide $|G|$. Let $m$ be the number of solutions of $x^n=1$. Prove that $n\mid m$.

Why is $A \rtimes B \simeq \mathbb Z \rtimes \mathbb Z/2\mathbb Z$

A prime ideal of $\mathbb{Z} \times \mathbb{Z}$ that is not maximal.

Showing that union over a collection of connected sets $\{F_n\}$ with $F_i\cap F_j \neq \varnothing, i\neq j$ is connected.

In search for easy counterexample of $L^2$ ineq. - if it exists

Prove that $F[x,y] / (y^2-x)$ is an integral domain

Is the order of a quotient of the multiplicative group of integers a prime power if the group is cyclic?

When two elements of a group generate the same subgroup

Finding points of discontinuity of $f(x)=\lim_{t\to\infty}\frac{|a+\sin(\pi x)|^t-1}{|a+\sin(\pi x)|^t+1}$

Let $G$ be a nonabelian group of order $p^{3},$ where $p$ is a prime. Show that $G$ has exactly $p^{2}+p-1$ distinct conjugacy classes.

To Prove $ \bigcap_{i \in I} A_i \in \bigcap_{i \in I} P(A_i) $

Understanding the biconditional logical connective in the set: $K = \{x \in G: x \circ a \circ x^{-1} \in H \iff a \in H \}$

In $\mathbb Z[x]$, find an ideal $P$ such that $R/P$ consists of $4$ elements.

Evaluating $\int_{0}^{1}\int_{0}^{1}\sqrt{x^{2}+y^{2}}dxdy$ using polar coordinates.

Show that $\langle x,y,z \rangle$ has order $42$ for $x,y,z$ with given properties

The number of subgroups of $Z_{p^2}$ $\oplus$ $Z_{p^2}$ which are isomorphic to $Z_{p^2}$.

If $n \geq 3$ then there is no surjective homomorphism $f: D_{2n} \to Z_n$.

Epimorphism from $\mathbb{Z}[i]$ to $\mathbb{F}_{p}$ where $p\equiv1 \pmod 4$

Preimage of subgroup $H \subseteq G/N$ has order $|H| \cdot |N|$

Why is it impossible for the mapping $x\mapsto 1/x$ to be a polynomial in an infinite field?

First isomorphism theorem $G=\mathbb{Z}/60\mathbb{Z}=<\overline{1}>$

How can i find a solution of this optimization problem?

Proving that $\bigcap \mathcal P\subseteq\left(\bigcap\mathcal M\right)\cup\left(\bigcup\mathcal N\right)$

Density of a countable union of rational lines