Intereting Posts

Is it possible to formalize all mathematics in terms of ordinals only?
Integral that arises from the derivation of Kummer's Fourier expansion of $\ln{\Gamma(x)}$
How do you prove Gautschi's inequality for the gamma function?
Proof that Epicycloids are Algebraic Curves?
Standard compactness argument
Prove an integral inequality $|\int\limits_0^1f(x)dx|\leq\frac{1-a+b}{4}M$
Show that $X = \{ (x,y) \in\mathbb{R}^2\mid x \in \mathbb{Q}\text{ or }y \in \mathbb{Q}\}$ is path connected.
An example of a Lindelöf topological space which is not $\sigma$-compact
If the tensor product of two modules is free of finite rank, then the modules are finitely generated and projective
Proof that $\mathbb{R}$ is not a finite dimensional vector space
Strictly diagonally dominant matrices are non singular
How to prove Mandelbrot set is simply connected?
Find all non-singular $3 \times 3$ matrices, such as $A$ and $A^{-1}$ elements are non-negative
An example for a calculation where imaginary numbers are used but don't occur in the question or the solution.
Is this matrix positive semi-definite?

Motivated by this problem, and KCd’s comment on my answer, I am left with the following question:

Question:Suppose that $n\not \equiv 2\pmod{3}$. Is $$x^n+x+1$$ irreducible over $\mathbb{Q}$?

I am not sure how to solve this, any thoughts are appreciated.

- Taking Calculus in a few days and I still don't know how to factorize quadratics
- Factoring multivariate polynomial
- Fermat's Last Theorem and Kummer's Objection
- Factoring $ac$ to factor $ax^2+bx+c$
- How to solve Diophantine equations of the form $Axy + Bx + Cy + D = N$?
- If I remove the premise $a\neq b$ in this question, will the statement still be true?

- Using Parseval' s theorem to evaluate a sum..
- Adjoining a number to a field
- What's so special about characteristic 2?
- Compositum of abelian Galois extensions is also?
- Unramified p-adic extension implies Galois
- Is $\mathbb{Q}$ the same as $\mathbb{Q}(\sqrt{2},\sqrt{3})$?
- Can a field be isomorphic to its subfield but not to a subfield in between?
- How do I prove that $X^{p^n}-X$ is the product of all monic irreducible polynomials of degree dividing $n$?
- What is difference between a ring and a field?
- Does $\varphi(1)=1$ if $\varphi$ is a field homomorphism?

Yes, it is true. See the second claim of Theorem 1 on page 289.

- An example of a regular function over an open set
- For what $(n,k)$ there exists a polynomial $p(x) \in F_2$ s.t. $\deg(p)=k$ and $p$ divides $x^n-1$?
- Integer coordinate set of points that is a member of sphere surface
- Identity for convolution of central binomial coefficients: $\sum\limits_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$
- Contour Integration – my solution for real integral is complex?
- Why is the Koch curve homeomorphic to $$?
- Why is an empty set not a terminal object in categories $\mathsf{Top}$ and $\mathsf{Sets}$?
- Proof that Newton Raphson method has quadratic convergence
- Group equals union of two subgroups
- Area of projection of cube in $\mathbb{Z}^3$ onto a hyperplane
- $I\otimes I$ is torsion free for a principal ideal $I$ in domain $R$
- Find a prime number $p$ and an integer $b<p$ such that $p$ divides $b^{p−1}−1$.
- computing ${{27^{27}}^{27}}^{27}\pmod {10}$
- How to prove this inequality $\frac{x^y}{y^x}+\frac{y^z}{z^y}+\frac{z^x}{x^z}\ge 3$
- Finding determinant for a matrix with one value on the diagonal and another everywhere else