User Watson - Mathematics Stack Exchange

29 votes

5 answers

2k views

Is there any perfect square in the sequence $12,123,1234,12345,...$?

asked Aug 24, 2016 at 21:10

27 votes

1 answer

1k views

Is there any palindromic power of $2$?

asked Feb 13, 2016 at 10:53

26 votes

1 answer

964 views

If $A[X] \cong B[X]$ as rings, are the degrees of irreducible polynomials the same in $A$ and in $B$?

asked Jul 25, 2016 at 20:42

22 votes

1 answer

640 views

Does $A^2 \cong B^2$ imply $A \cong B$ for rings?

asked Jul 24, 2016 at 14:11

21 votes

2 answers

6k views

Quotient ring of Gaussian integers $\mathbb{Z}[i]/(a+bi)$ when $a$ and $b$ are NOT coprime

asked Jul 23, 2016 at 10:00

20 votes

4 answers

878 views

Is there no formula for $\cos(x^2)$?

asked Feb 4, 2016 at 15:15

19 votes

0 answers

853 views

Is there a field $F$ which is isomorphic to $F(X,Y)$ but not to $F(X)$?

asked Nov 5, 2016 at 10:47

18 votes

1 answer

1k views

Variation of the Kempner series – convergence of series $\sum\frac{1}{n}$ where $9$ is not a digit of $1/n$.

asked Feb 6, 2016 at 17:36

18 votes

1 answer

986 views

Is $0.248163264128…$ a transcendental number?

asked Feb 17, 2016 at 10:03

17 votes

0 answers

401 views

Swapping the digits of an algebraic number (e.g. $\sqrt 2$)

asked Feb 15, 2016 at 14:23

15 votes

1 answer

794 views

The four runner problem/conjecture

asked Dec 20, 2015 at 19:06

15 votes

1 answer

1k views

Algebraic fixed point theorem

asked Dec 27, 2015 at 9:44

14 votes

1 answer

481 views

Is there a topology such that $(\Bbb R, +, \mathcal T)$ is a compact Hausdorff topological group?

asked Jul 21, 2016 at 19:58

13 votes

2 answers

1k views

Finding the ring of integers of $\Bbb Q(\sqrt[4]{2})$

asked Jul 23, 2016 at 14:40

13 votes

1 answer

732 views

Isomorphism between $\Bbb R$ and $\Bbb R(X)$?

asked Aug 19, 2016 at 16:01

13 votes

2 answers

2k views

Rings with a given number of (prime, maximal) ideals

asked Oct 5, 2016 at 12:38

13 votes

1 answer

358 views

Algebraic extension of $\Bbb Q$ with exactly one extension of given degree $n$

asked Feb 2, 2017 at 13:20

12 votes

1 answer

198 views

Multiple of real numbers with only $0$'s and $1$'s in the integer part

asked Sep 16, 2016 at 18:01

12 votes

1 answer

546 views

Is there a field extension $K / \Bbb Q$ such that $\text{Aut}_{\Bbb Q}(K) \cong \Bbb Z$?

asked Jul 26, 2016 at 10:04

12 votes

3 answers

1k views

Is $\Bbb Q(\sqrt 2, e)$ a simple extension of $\Bbb Q$?

asked Aug 17, 2016 at 19:06

12 votes

1 answer

1k views

Module which is not direct sum of indecomposable submodules

asked Dec 14, 2015 at 19:16

12 votes

0 answers

722 views

Properties of King's Dream fractal

asked Dec 15, 2015 at 20:58

11 votes

1 answer

2k views

Totally real Galois extension of given degree

asked Jul 22, 2016 at 19:06

10 votes

1 answer

656 views

Roots of iterations of polynomials

asked Feb 5, 2016 at 21:29

10 votes

1 answer

2k views

What is the minimal number of generators of the ideal $(6x, 10x^2, 15x^3)$ in $\Bbb Z[x]$?

asked Aug 15, 2016 at 19:05

10 votes

4 answers

833 views

Proving $\int_0^1 \frac{(\ln(x))^5}{1+x} \mathrm{d}x = -\frac{31\pi^6}{252}$

asked Jan 27, 2017 at 20:15

10 votes

0 answers

111 views

If the number of points of two elliptic curves are close enough, then they are equal?

asked Nov 6, 2018 at 9:11

10 votes

0 answers

198 views

Is there a notion of polynomial ring in "one half variable"?

asked Dec 2, 2019 at 7:33

9 votes

2 answers

2k views

Absolute Galois group of $\Bbb Q_p$ while varying $p$

asked Jul 8, 2018 at 20:28

9 votes

2 answers

712 views

Is $\Bbb Z_p^2$ a Galois group over $\Bbb Q$?

asked Jul 13, 2018 at 9:42

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131 Questions

Is there any perfect square in the sequence $12,123,1234,12345,...$?

Is there any palindromic power of $2$?

If $A[X] \cong B[X]$ as rings, are the degrees of irreducible polynomials the same in $A$ and in $B$?

Does $A^2 \cong B^2$ imply $A \cong B$ for rings?

Quotient ring of Gaussian integers $\mathbb{Z}[i]/(a+bi)$ when $a$ and $b$ are NOT coprime

Is there no formula for $\cos(x^2)$?

Is there a field $F$ which is isomorphic to $F(X,Y)$ but not to $F(X)$?

Variation of the Kempner series – convergence of series $\sum\frac{1}{n}$ where $9$ is not a digit of $1/n$.

Is $0.248163264128…$ a transcendental number?

Swapping the digits of an algebraic number (e.g. $\sqrt 2$)

The four runner problem/conjecture

Algebraic fixed point theorem

Is there a topology such that $(\Bbb R, +, \mathcal T)$ is a compact Hausdorff topological group?

Finding the ring of integers of $\Bbb Q(\sqrt[4]{2})$

Isomorphism between $\Bbb R$ and $\Bbb R(X)$?

Rings with a given number of (prime, maximal) ideals

Algebraic extension of $\Bbb Q$ with exactly one extension of given degree $n$

Multiple of real numbers with only $0$'s and $1$'s in the integer part

Is there a field extension $K / \Bbb Q$ such that $\text{Aut}_{\Bbb Q}(K) \cong \Bbb Z$?

Is $\Bbb Q(\sqrt 2, e)$ a simple extension of $\Bbb Q$?

Module which is not direct sum of indecomposable submodules

Properties of King's Dream fractal

Totally real Galois extension of given degree

Roots of iterations of polynomials

What is the minimal number of generators of the ideal $(6x, 10x^2, 15x^3)$ in $\Bbb Z[x]$?

Proving $\int_0^1 \frac{(\ln(x))^5}{1+x} \mathrm{d}x = -\frac{31\pi^6}{252}$

If the number of points of two elliptic curves are close enough, then they are equal?

Is there a notion of polynomial ring in "one half variable"?

Absolute Galois group of $\Bbb Q_p$ while varying $p$

Is $\Bbb Z_p^2$ a Galois group over $\Bbb Q$?