User MathEric

46 votes

4 answers

2k views

Does the sequence $n+\tan(n), n \in\mathbb{N}$ have a lower bound?

asked Jun 15, 2018 at 3:02

37 votes

3 answers

18k views

Why is the norm of a matrix larger than its eigenvalue?

asked Jul 18, 2018 at 0:00

10 votes

2 answers

575 views

Why is Axiom of Choice "a convenient and safe labour-saving device"?

asked Jun 9, 2018 at 7:21

9 votes

2 answers

230 views

If $N$ is large enough, then $x^5-Nx+1$ and $x^5-Nx^2+1$ are irreducible over $\mathbb{Q}$.

asked Feb 29, 2020 at 10:45

8 votes

1 answer

160 views

$a^n-1$ and $b^n-1$ have the same set of prime factors for each $n\in\Bbb{Z}^+$, show that $a=b$.

asked Oct 30, 2020 at 21:39

8 votes

2 answers

474 views

$\forall x\in [0,1]$, if $f(t)f(t-x)$ is integrable, then $f(t)$ is integrable?

asked Aug 15, 2018 at 18:42

7 votes

2 answers

3k views

Why is Axiom of Pairing needed?

asked Jun 8, 2018 at 22:48

6 votes

1 answer

232 views

For any positive integer $k$, there exists a prime $p$ such that ${x \choose k}\equiv -1\pmod{p}$ has an integer solution.

asked Jul 1, 2020 at 12:11

6 votes

1 answer

303 views

Infinitely many common prime divisors

asked Jul 2, 2020 at 3:39

5 votes

1 answer

275 views

Prove the coefficients of $\prod_{k=2}^{n+1}(1-x^{a_k})$ are $0$, $1$, or $-1$ where $(a_k)$ are Fibonacci numbers.

asked May 4, 2018 at 21:38

5 votes

1 answer

184 views

Can we remove the absolute value when doing Diophantine Approximation?

asked Jun 28, 2018 at 3:22

5 votes

2 answers

2k views

Points of a dense set are not limit points

asked Jul 6, 2018 at 4:51

5 votes

2 answers

254 views

How to prove $\sum_{i=1}^{p-1}\sqrt[p]{\frac{i}{p}} $ is an algebraic integer?

asked May 27, 2019 at 9:01

4 votes

1 answer

99 views

For any cardinal numbers $a\neq b$, is there a cardinal number $c$ such that $c^a\neq c^b$?

asked Feb 6, 2021 at 1:48

4 votes

2 answers

208 views

How to find the degree of the extension $[\mathbb{Q}(\sqrt[4]{3+2\sqrt{5}}):\mathbb{Q}]$?

asked May 31, 2020 at 10:02

3 votes

3 answers

143 views

How to prove or disprove the following set is compact?

asked Oct 28, 2018 at 2:39

3 votes

1 answer

200 views

Show that the center of a group is an invariant subgroup using symmetry

asked Dec 31, 2019 at 20:59

3 votes

0 answers

50 views

How to prove if $\bigcup_{k=1}^{n}V_{k}$ is a subspace over $\mathbb{C}$ then $\bigcup_{k=1}^{n}V_{k}=V_{j}$ for some j? [duplicate]

asked Oct 8, 2018 at 21:28

2 votes

1 answer

122 views

How to prove by inudction if $\bigcup_{k=1}^{n}V_{k}$ is a subspace over $\mathbb{C}$ then $\bigcup_{k=1}^{n}V_{k}=V_{j}$ for some j?

asked Oct 9, 2018 at 3:49

2 votes

1 answer

153 views

Question about Hungerford's definition about cardinality

asked Oct 13, 2018 at 1:12

2 votes

2 answers

218 views

Question about the definition of a free abelian group

asked Aug 27, 2019 at 0:18

2 votes

1 answer

761 views

How to find all solutions of the ODE $x'=3x^{\frac{2}{3}}, x(0)=0$

asked Jul 25, 2018 at 16:43

2 votes

2 answers

148 views

Find the minimal maximal distance in a $n\times n$ square grid? [duplicate]

asked Jun 16, 2020 at 19:59

2 votes

1 answer

130 views

Find the maximal minimum distance in a $n\times n$ square grid?

asked Jun 23, 2020 at 21:01

1 vote

1 answer

70 views

Congruence equation with binomial coefficient

asked Jun 30, 2020 at 17:45

1 vote

0 answers

48 views

How to prove an ideal is prime in $R[x]$ when $R$ is not an integral domain?

asked Feb 13, 2020 at 4:04

1 vote

1 answer

77 views

How to show the following cubic graph is Hamiltonian?

asked Jun 3, 2020 at 6:09

1 vote

1 answer

315 views

Can the ''Galois group" for an inseparable irreducible polynomial of degree 4 be $S_{3}$?

asked May 3, 2020 at 11:12

1 vote

1 answer

82 views

The series$\sum\limits_{n=1}^{\infty}(\frac{(2n-1)!!}{(2n)!!})^p$ converges if and only if $p>2$

asked May 12, 2018 at 5:53

1 vote

1 answer

354 views

How to prove there is left\right adjoint for non-degenerate bilinear form?

asked May 17, 2018 at 2:11

Stack Exchange Network

41 Questions

Does the sequence $n+\tan(n), n \in\mathbb{N}$ have a lower bound?

Why is the norm of a matrix larger than its eigenvalue?

Why is Axiom of Choice "a convenient and safe labour-saving device"?

If $N$ is large enough, then $x^5-Nx+1$ and $x^5-Nx^2+1$ are irreducible over $\mathbb{Q}$.

$a^n-1$ and $b^n-1$ have the same set of prime factors for each $n\in\Bbb{Z}^+$, show that $a=b$.

$\forall x\in [0,1]$, if $f(t)f(t-x)$ is integrable, then $f(t)$ is integrable?

Why is Axiom of Pairing needed?

For any positive integer $k$, there exists a prime $p$ such that ${x \choose k}\equiv -1\pmod{p}$ has an integer solution.

Infinitely many common prime divisors

Prove the coefficients of $\prod_{k=2}^{n+1}(1-x^{a_k})$ are $0$, $1$, or $-1$ where $(a_k)$ are Fibonacci numbers.

Can we remove the absolute value when doing Diophantine Approximation?

Points of a dense set are not limit points

How to prove $\sum_{i=1}^{p-1}\sqrt[p]{\frac{i}{p}} $ is an algebraic integer?

For any cardinal numbers $a\neq b$, is there a cardinal number $c$ such that $c^a\neq c^b$?

How to find the degree of the extension $[\mathbb{Q}(\sqrt[4]{3+2\sqrt{5}}):\mathbb{Q}]$?

How to prove or disprove the following set is compact?

Show that the center of a group is an invariant subgroup using symmetry

How to prove if $\bigcup_{k=1}^{n}V_{k}$ is a subspace over $\mathbb{C}$ then $\bigcup_{k=1}^{n}V_{k}=V_{j}$ for some j? [duplicate]

How to prove by inudction if $\bigcup_{k=1}^{n}V_{k}$ is a subspace over $\mathbb{C}$ then $\bigcup_{k=1}^{n}V_{k}=V_{j}$ for some j?

Question about Hungerford's definition about cardinality

Question about the definition of a free abelian group

How to find all solutions of the ODE $x'=3x^{\frac{2}{3}}, x(0)=0$

Find the minimal maximal distance in a $n\times n$ square grid? [duplicate]

Find the maximal minimum distance in a $n\times n$ square grid?

Congruence equation with binomial coefficient

How to prove an ideal is prime in $R[x]$ when $R$ is not an integral domain?

How to show the following cubic graph is Hamiltonian?

Can the ''Galois group" for an inseparable irreducible polynomial of degree 4 be $S_{3}$?

The series$\sum\limits_{n=1}^{\infty}(\frac{(2n-1)!!}{(2n)!!})^p$ converges if and only if $p>2$

How to prove there is left\right adjoint for non-degenerate bilinear form?