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Mathematics
zeraoulia rafik's user avatar
zeraoulia rafik's user avatar
zeraoulia rafik's user avatar
zeraoulia rafik
  • Member for 9 years, 5 months
  • Last seen more than 7 years ago
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i'm a teacher in high school ,interesting to math number theory and dynamical systems soo ...

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question
37
Is this $\gcd(0, 0) = 0$ a wrong belief in mathematics or it is true by convention?
Aug 6, 2015
question
20
Infinite sum of reciprocals of pentagonal numbers
May 30, 2015
answer
17
Prove that:$\sum_{i=1}^n\frac{1}{x_i}-\sum_{i<j}\frac{1}{x_i+x_j}+\sum_{i<j<k}\frac{1}{x_i+x_j+x_k}-\cdots+(-1)^{n-1}\frac{1}{x_1+\ldots+x_n}>0.$?
Jun 29, 2015
question
14
How i show this beautiful inequality :$\frac{x^n}{x^m+y^m}+\frac{y^n}{y^m+z^m}+\frac{z^n}{z^m+x^m}\geq \frac{3} {2}(\frac{1}{\sqrt{3}})^{n-m}$?
May 31, 2015
answer
14
How do I evaluate $\lim_{n\rightarrow \infty}\frac{1}{\sqrt{n}}\sum_{k=1}^{n}\frac{1}{\sqrt{k}}$?
Jul 4, 2015
question
11
For which values of $\theta$ does this equation $x^{\cos\theta} +y^{\sin\theta }=1$ have solutions in integers?
May 28, 2015
question
10
How do i evaluate this sum $\sum\limits_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^2n!}$?
Dec 14, 2015
answer
9
How do I evaluate this integral $I = \int_{0}^{2 \pi} \ln (\sin x +\sqrt{1+\sin^2 x}) dx$?
Jun 29, 2015
question
7
Is there a polynomial $p$ such that it is bijective and $ p: \mathbb{Q}^n \rightarrow \mathbb{Q}$ for $ n>1$ ??
Aug 3, 2015
question
6
How do I convince students in high school for which this equation: $2^x=4x$ have only one solution in integers that is $x=4$?
Aug 9, 2015
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12
Is there a fixed integer $x>1$ satisfing ${\sigma}^{k}(x)\equiv 0\pmod{x}$ for all positive integers $k$?
6
Is $\liminf \frac{\sigma_{k}(n)}{n}$ finite for every $k$?