Beni Bogosel

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21671
bio website mathproblems123.wordpress.com
location Chambery, France
age 25
visits member for 2 years, 3 months
seen Apr 24 at 21:47
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PHD - interests: PDE, Free boundaries, Shape Optimization


271 Answers

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20
Elementary proof of $m^n\neq n^m$ for almost all natural numbers $m\neq n$
17
For complex $z$, $|z| = 1 \implies \text{Re}\left(\frac{1-z}{1+z}\right) = 0$
17
Inequality: $(x + y + z)^3 \geq 27 xyz$
14
How are the integral parts of $(9 + 4\sqrt{5})^n$ and $(9 − 4\sqrt{5})^n$ related to the parity of $n$?
13
Evaluating $\displaystyle\lim_{x \to 0}\frac{1-\cos (1- \cos x)}{x^4}$
13
Find x in $4^{\sin^2x}+4^{\cos^2x}=8$
12
Does $F(t)F'(t) \le 0$ imply that $F$ does not change signs?
12
$\lim_{n \to +\infty } \left \{ en! \right \}$
11
Solving the system $\sum \sin = \sum \cos = 0$.
11
How to prove periodicity of $\sin(x)$ or $\cos(x)$ starting from the Taylor series expansion?
11
Proving that $ 2 $ is the only real solution of $ 3^x+4^x=5^x $
11
limit of a recursively defined function
10
If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
10
Prove that $f(x)$ has no integer roots
9
Example that $\int |f(x)| dx=\infty$ but $\int |f(x)|^2 dx <\infty$
9
Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?
9
Prove that if two miles are run in 7:59 then one mile MUST be run under 4:00.
9
Show that $f(x+y)=f(x)+f(y)$ implies $f$ continuous $\Leftrightarrow$ $f$ measurable
8
Linear Algebra Textbook
8
Intuition behind problem in (classical) algebra
8
What is the solution of cos(x)=x?
8
Solving for the implicit function $f\left(f(x)y+\frac{x}{y}\right)=xyf\left(x^2+y^2\right)$ and $f(1)=1$
7
Showing that $ \frac{x\sin(y)-y\sin(x)}{x^2+y^2}\rightarrow_{(x,y)\to (0,0)}0$
7
Which internal angles can a lattice polygon have?
7
Showing the derivative of a differentiable function has a point of continuity
6
Manual integration by parts
6
Inequality. $abc(a+b+c) > 3abc+ab+bc+ca.$
6
No invertible matrix
6
$ \lim\limits_{n \to{+}\infty}{\sqrt[n]{n!}}$ is infinite
6
An application of Vandermonde determinant
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