User leoli1

15 votes

What's the most elementary way to solve this trigonometric problem?

answered Jan 2, 2021 at 10:36

10 votes

Accepted

Is every injective ring homomorphism an automorphism?

answered Jan 29, 2021 at 15:49

8 votes

Accepted

Proving the properties of polynomial functions without using calculus

answered Aug 16, 2021 at 17:14

7 votes

Accepted

The Diophantine equation $x^5-2y^2=1$

answered Aug 7, 2021 at 1:45

6 votes

Accepted

$S^{n + m}$ is not homeomorphic to $M \times N$

answered Jan 8, 2021 at 8:57

6 votes

Accepted

Evaluate $\prod_{p \in \mathbb{P}} \left( 1 + \frac{3p^2}{(p^2 - 1)^2} \right)$ for prime numbers $p$, where $p = 14k \pm 1$ or $p = 18k \pm 1$

answered Aug 29, 2021 at 13:11

5 votes

Accepted

Prove that $A$, a matrix of rank $3$, can't have characteristic polynomial of $p(x) = x^7 - x^5 + x^3$

answered Jan 9, 2021 at 10:32

5 votes

Accepted

Inverses in $\mathbb{Z}[\zeta_p]$

answered Jan 14, 2021 at 20:21

5 votes

Accepted

If $\lim_{x \to a} f\left(x\right) = L$ then does $\lim_{x \to L} f^{-1}\left(x\right) = a$

answered Jan 15, 2021 at 10:20

5 votes

Prove that $(1+\frac{1}{n})^k < 1+ \frac{k}{n}+\frac{k^2}{n^2}$

answered Jan 19, 2021 at 10:50

5 votes

Accepted

If for every sequence $(x_n)$, $x_n \to x_0 \implies (f(x_n))$ is a Cauchy sequence, then is $f$ continuous?

answered Jan 20, 2021 at 10:42

5 votes

Accepted

"Reducing" spliting fields

answered Jan 28, 2021 at 17:14

5 votes

Accepted

Prove that $\angle AEF =90^\circ$ given a square $ABCD$

answered Feb 8, 2021 at 19:56

5 votes

Accepted

class number of $\mathcal O_D$ is odd for $D\equiv1 \pmod 4$, quadratic imaginary fields

answered Sep 30, 2021 at 19:35

5 votes

Accepted

Are all rings of integers closed under conjugation?

answered Apr 6, 2021 at 21:04

4 votes

Accepted

A Dedekind Domain if and only if localizations at all nonzero primes are DVRs

answered Feb 14, 2021 at 20:12

4 votes

Accepted

Existence of Intermediate field $F$ of $E$ and $G$ such that the $[G: F] < \infty$

answered Feb 21, 2021 at 12:00

4 votes

Accepted

Field extension of $\Bbb Q$ of degree $4$ has reals

answered Feb 26, 2021 at 10:59

4 votes

Accepted

Prove that $E[F]$ is not a field.

answered Jan 29, 2021 at 22:37

4 votes

Accepted

Try to choose a special number $t$ which satisify $\eta(f(x))=f(t)$

answered Jan 30, 2021 at 13:03

4 votes

Accepted

$f(c)<1/(b-a)\int^b_a f(x)dx<f(c')$

answered Jan 30, 2021 at 20:53

4 votes

Accepted

Find two functions f,g such that $f(n)∼g(n)$ and $f(n)^n=o(g(n)^n)$

answered Jan 20, 2021 at 21:11

4 votes

Finding a function which is not differentiable at $x_{0}$

answered Jan 16, 2021 at 16:14

4 votes

Numbers that can be expressed as $ab + a + b$

answered Jan 16, 2021 at 21:34

4 votes

Accepted

Is every normal subgroup of $G$ of this form?

answered Jan 17, 2021 at 19:19

4 votes

Accepted

List of all $\mathbb{C}[X]$ modules?

answered Jan 15, 2021 at 10:02

4 votes

Find the value of $k$ in $\frac{b+c}{\sqrt{a}}+\frac{c+a}{\sqrt{b}}+\frac{a+b}{\sqrt{c}} \ge \sqrt{a}+\sqrt{b}+\sqrt{c}+k$

answered Jan 14, 2021 at 13:15

4 votes

Accepted

Property of the $\zeta := \exp(2\pi i/k)$ function.

answered Jan 13, 2021 at 12:36

4 votes

Accepted

Show $\overline{\oint_{\gamma}f(z)dz} =- \oint_{\gamma}\overline{f(z)}\cdot z^{-2}dz$

answered Jan 11, 2021 at 18:17

4 votes

Accepted

$f(z)$ is holomorphic on $|z| < 1$, with $|f(z)| ≤ 3$ and $f(\frac{1}{2}) = 2$. Show that $f(z) \neq 0$ when $|z| < \frac{1}{8}.$

answered Aug 7, 2021 at 1:02

Stack Exchange Network

212 Answers

What's the most elementary way to solve this trigonometric problem?

Is every injective ring homomorphism an automorphism?

Proving the properties of polynomial functions without using calculus

The Diophantine equation $x^5-2y^2=1$

$S^{n + m}$ is not homeomorphic to $M \times N$

Evaluate $\prod_{p \in \mathbb{P}} \left( 1 + \frac{3p^2}{(p^2 - 1)^2} \right)$ for prime numbers $p$, where $p = 14k \pm 1$ or $p = 18k \pm 1$

Prove that $A$, a matrix of rank $3$, can't have characteristic polynomial of $p(x) = x^7 - x^5 + x^3$

Inverses in $\mathbb{Z}[\zeta_p]$

If $\lim_{x \to a} f\left(x\right) = L$ then does $\lim_{x \to L} f^{-1}\left(x\right) = a$

Prove that $(1+\frac{1}{n})^k < 1+ \frac{k}{n}+\frac{k^2}{n^2}$

If for every sequence $(x_n)$, $x_n \to x_0 \implies (f(x_n))$ is a Cauchy sequence, then is $f$ continuous?

"Reducing" spliting fields

Prove that $\angle AEF =90^\circ$ given a square $ABCD$

class number of $\mathcal O_D$ is odd for $D\equiv1 \pmod 4$, quadratic imaginary fields

Are all rings of integers closed under conjugation?

A Dedekind Domain if and only if localizations at all nonzero primes are DVRs

Existence of Intermediate field $F$ of $E$ and $G$ such that the $[G: F] < \infty$

Field extension of $\Bbb Q$ of degree $4$ has reals

Prove that $E[F]$ is not a field.

Try to choose a special number $t$ which satisify $\eta(f(x))=f(t)$

$f(c)<1/(b-a)\int^b_a f(x)dx<f(c')$

Find two functions f,g such that $f(n)∼g(n)$ and $f(n)^n=o(g(n)^n)$

Finding a function which is not differentiable at $x_{0}$

Numbers that can be expressed as $ab + a + b$

Is every normal subgroup of $G$ of this form?

List of all $\mathbb{C}[X]$ modules?

Find the value of $k$ in $\frac{b+c}{\sqrt{a}}+\frac{c+a}{\sqrt{b}}+\frac{a+b}{\sqrt{c}} \ge \sqrt{a}+\sqrt{b}+\sqrt{c}+k$

Property of the $\zeta := \exp(2\pi i/k)$ function.

Show $\overline{\oint_{\gamma}f(z)dz} =- \oint_{\gamma}\overline{f(z)}\cdot z^{-2}dz$

$f(z)$ is holomorphic on $|z| < 1$, with $|f(z)| ≤ 3$ and $f(\frac{1}{2}) = 2$. Show that $f(z) \neq 0$ when $|z| < \frac{1}{8}.$