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Zerox's user avatar
Zerox
  • Member for 4 years, 3 months
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7 votes

Solve in rational numbers, the equation, $x\lfloor x\rfloor\{x\}=58$

6 votes

Is the limit of approximate eigenvectors an eigenvector?

5 votes

Let a, b, c be ints. $\frac{ab}{c} + \frac{bc}{a} + \frac{ac}{b}$ is an int, show that each of $\frac{ab}{c}, \frac{bc}{a}, \frac{ac}{b}$ is an int.

5 votes
Accepted

Proving $\int_0^1(1-x^n)^{\frac{1}{m}}dx=\int_0^1(1-x^m)^{\frac{1}{n}}dx$ Without Using Beta Function

4 votes

Determine all $P(x) \in \mathbb R[x]$ such that $P(x^2) + x\big(mP(x) + nP(-x)\big) = \big(P(x)\big)^2 + (m - n)x^2$, $\forall x \in \mathbb R$.

4 votes

If $\ (X,d)\ $ is a complete metric space, and $\ A\ $ is a closed, convex subset of $\ X,\ $ then is $\ A\ $ connected?

4 votes

Let $(x-a)^2 +(x-b)^2 =(x-a)^2(x-b)^2$ have three roots then find $|a-b|$.

2 votes
Accepted

Find a $(X,\mathscr{A})$ and finite measures $\mu$ and $\nu$ such that $\mu(X)=\nu(X)$ but $\{A\in\mathscr{A}:\mu(A)=\nu(A)\}$ not a sigma algebra

2 votes

How do you solve $\lim_{n\to\infty}\left(\frac{\log(n+1)}{\log(n)}\right)^{n\log(n)}$

2 votes
Accepted

Show that there exists $A$ $(n×n)$ matrix with complex entries such that...

2 votes
Accepted

Determine the polynomials $P \in \mathbb{R}[X] $ such that : $X^n$ divides $X + 1 − P^2$.

2 votes
Accepted

Normal bundle of a non-orientable manifold

2 votes
Accepted

If x, y and z are rational and strictly positive and if $\frac{1}{x} + \frac{1}{y} = \frac{1}{z}$, show that $\sqrt{x^2+y^2+z^2}$ is rational

2 votes
Accepted

The set of real numbers whose product is rational is Borel in $\mathbb{R}^2$

2 votes

If for invertible matrices $A$ and $X$, $XAX^{-1}=A^2$ then eigenvalues of $A$ are $n^{th}$ roots of unity.

2 votes

Completely factoring $a^3 + b^3 + c^3 - 3abc$?

2 votes
Accepted

In any triangle, $b^2\sin(2\gamma)+c^2\sin(2\beta)=2ac\sin(\beta)$

1 vote

Find the area of ​the shaded region in the triangle below?

1 vote
Accepted

Find a counter example for the convergence of a sequence that has a property close from cauchy

1 vote

Prove that $C+C=[0,2]$, where $C$ is the Cantor set.

1 vote

Given three general lines in $\Bbb{R}^3$, can we construct the center and median plane of the one-sheet hyperboloid they determine?

1 vote
Accepted

Equivalence of definitions of collineations.

1 vote
Accepted

Find $\psi\in C^1(\mathbb{R},\mathbb{R})$ such that $\psi^3+e^x\cdot\psi=id$

1 vote
Accepted

Let $f:\mathbb{R}^2 \rightarrow \mathbb{R}^2$ such that $f(a,b)=(b,0)$. Show that $Ker f = Im f$

1 vote

Find the minimum value of $(\tan C – \sin A)^2 + (\cot C – \cos B)^2$ for the following given data

1 vote

Bounded operators: $\langle T_n (x),x \rangle \longrightarrow 0 \implies T_n (x) \rightarrow 0$?

1 vote
Accepted

Are there absolute value of field, which is not discrete in $\Bbb{R}_{>0}^×$, and also not dense in $\Bbb{R}_{>0}^×$?

1 vote
Accepted

When is $\|f(x) - y\|$ a smooth function?

1 vote

Inequality with real exponents

1 vote
Accepted

Doubts in the proof that a subgroup $H$ of a Lie group $G$ that is a submanifold of $G$ is (topologically) closed in $G$