# All Questions

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### Let $∑_{n=0}^∞c_n z^n$ be a representation for the function $\frac{1}{1-z-z^2 }$. Find the coefficient $c_n$

Let $∑_{n=0}^∞c_n z^n$ be a power series representation for the function $\frac{1}{1-z-z^2 }$. Find the coefficient $c_n$ and radius of convergence of the series. Clearly this is a power series with ...
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### the infinite sum of symmetric random variables is also symmetric

Definition. Let $(\Omega, {\mathcal F}, \mathbb{P})$ be a probability space and $X$ a random variable in $\Omega$. $X$ is said to be ${\mathbf symmetric}$ (about $0$) if $X$ and $-X$ are equal in law....
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### there exsit postive integer $x,y$ such $p\mid(x^2+y^2+n)$ [duplicate]

For any give the postive integer $n$,and for any give prime number $p$. show that there exsit postive integer $x,y$ such $$p\mid(x^2+y^2+n)$$ My approach is the following: Assmue that $n=1,p=2$,...
### Is there a $k$ such that $2^n$ has $6$ as one of its digits for all $n\ge k$?
It is true that every power of $2$ of the form $2^{6+10x}$, $x\in\mathbb{N}$, has $6$ as one of its digits. Something more is true, the last two digits are either $64$ or $36$. The OP suggests that "....