User Ege Erdil

40 votes

The square roots of different primes are linearly independent over the field of rationals

answered May 28, 2016 at 20:17

38 votes

Accepted

Calculate $\int_{0}^{1} (x-f(x))^{2016} dx$, given $f(f(x))=x$.

answered May 8, 2016 at 14:22

37 votes

Are there infinitely many primes $p$ such that $p-2$ and $p+2$ are composite?

answered Oct 5, 2016 at 22:20

26 votes

Accepted

Elementary solution of exponential Diophantine equation $2^x - 3^y = 7$.

answered Sep 25, 2016 at 21:51

17 votes

Accepted

Why does "solvability" for groups suggest something about the solution of polynomials?

answered Apr 18, 2017 at 21:35

15 votes

Accepted

an odd degree polynomial with cyclic Galois group has root all real

answered May 2, 2018 at 3:59

14 votes

Why is $ (2+\sqrt{3})^n+(2-\sqrt{3})^n$ an integer?

answered Aug 25, 2016 at 10:34

13 votes

Accepted

Is the difference of two irrationals which are each contained under a single square root irrational?

answered Aug 21, 2016 at 18:22

11 votes

Does there exist a basis for the set of $2\times 2$ matrices such that all basis elements are invertible?

answered Nov 5, 2016 at 16:02

11 votes

Accepted

How many elements of $S_9$ commute with $(123)(4567)$?

answered Feb 6, 2017 at 9:22

11 votes

is $\sqrt[n]{n!}$ ever an integer?

answered Sep 18, 2016 at 0:52

10 votes

Accepted

Find a polynomial over $\mathbb{Q}$ with a given Galois group.

answered Apr 24, 2017 at 19:17

10 votes

Are there unsolved indeterminate limits?

answered May 12, 2020 at 18:18

9 votes

Irreducibility of polynomials in two variables

answered Mar 1, 2017 at 13:41

9 votes

Accepted

How to factorize $5$ in $\mathbb{Z}[\root 3 \of 2]$?

answered Sep 12, 2016 at 21:48

9 votes

Prove that $\sin x \cdot \sin (2x) \cdot \sin(3x) < \tfrac{9}{16}$ for all $x$

answered May 29, 2016 at 12:27

9 votes

Accepted

Is $\frac{1010103010101}9$ prime or composite?

answered May 6, 2016 at 20:11

9 votes

Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.

answered May 6, 2016 at 20:32

9 votes

Accepted

Why does the name "epimorphism" refer to a surjective homorphism?

answered May 14, 2016 at 18:12

8 votes

Accepted

If $[\overline F : F] = \infty$, does $F$ have extension of degree $n$ for any $n \geq 1$?

answered Feb 1, 2017 at 15:15

8 votes

Accepted

Galois group of $f(x^2)$

answered Oct 9, 2016 at 14:29

8 votes

Accepted

Is $x^{2^{n+1}} - x^{2^n} + 1$ is irreducible over the integers for all $n$?

answered May 4, 2017 at 2:17

8 votes

Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?

answered Jul 14, 2016 at 16:48

8 votes

What is $\mathbb{R}/\mathbb{Z}$ going to be?

answered May 6, 2016 at 11:29

8 votes

Let $p$ be a prime so $p\equiv3\pmod4$. If $p|a^2+b^2$, then $p|a,b$

answered Sep 16, 2016 at 18:57

8 votes

Product of one minus the tenth roots of unity

answered Aug 31, 2016 at 6:30

8 votes

Accepted

Method to determine if a ring is a UFD?

answered Aug 23, 2016 at 12:15

7 votes

Accepted

Prove that a finitely-generated free module has a finite basis

answered May 11, 2017 at 18:16

7 votes

Find positive integer $x,y$ such that $7^{x}-3^{y}=4$

answered Sep 30, 2016 at 11:45

7 votes

Accepted

Are there irreducible polynomials that are partially solvable by radicals?

answered Dec 30, 2016 at 21:34

Stack Exchange Network

448 Answers

The square roots of different primes are linearly independent over the field of rationals

Calculate $\int_{0}^{1} (x-f(x))^{2016} dx$, given $f(f(x))=x$.

Are there infinitely many primes $p$ such that $p-2$ and $p+2$ are composite?

Elementary solution of exponential Diophantine equation $2^x - 3^y = 7$.

Why does "solvability" for groups suggest something about the solution of polynomials?

an odd degree polynomial with cyclic Galois group has root all real

Why is $ (2+\sqrt{3})^n+(2-\sqrt{3})^n$ an integer?

Is the difference of two irrationals which are each contained under a single square root irrational?

Does there exist a basis for the set of $2\times 2$ matrices such that all basis elements are invertible?

How many elements of $S_9$ commute with $(123)(4567)$?

is $\sqrt[n]{n!}$ ever an integer?

Find a polynomial over $\mathbb{Q}$ with a given Galois group.

Are there unsolved indeterminate limits?

Irreducibility of polynomials in two variables

How to factorize $5$ in $\mathbb{Z}[\root 3 \of 2]$?

Prove that $\sin x \cdot \sin (2x) \cdot \sin(3x) < \tfrac{9}{16}$ for all $x$

Is $\frac{1010103010101}9$ prime or composite?

Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.

Why does the name "epimorphism" refer to a surjective homorphism?

If $[\overline F : F] = \infty$, does $F$ have extension of degree $n$ for any $n \geq 1$?

Galois group of $f(x^2)$

Is $x^{2^{n+1}} - x^{2^n} + 1$ is irreducible over the integers for all $n$?

Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?

What is $\mathbb{R}/\mathbb{Z}$ going to be?

Let $p$ be a prime so $p\equiv3\pmod4$. If $p|a^2+b^2$, then $p|a,b$

Product of one minus the tenth roots of unity

Method to determine if a ring is a UFD?

Prove that a finitely-generated free module has a finite basis

Find positive integer $x,y$ such that $7^{x}-3^{y}=4$

Are there irreducible polynomials that are partially solvable by radicals?