functional analysis - How to show that $p_{K}(x)<1$ iff $x$ is an ...
2019年9月24日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
linear algebra - Find a basis of the $k$ vector space $k(x ...
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probability - How to prove that $P (X ≥ k) = (1 - p)^k$? Can I start ...
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$p(p+1)=x^5-1$ where $p$ is a prime - Mathematics Stack …
2025年2月19日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
abstract algebra - Freshman's dream: $(x+y)^p = x^p+y^p$ in a ...
2019年12月28日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Common factors of the ideals $(x - \\zeta_p^k)$, $x \\in \\mathbb …
In the world of ideals gcd is the sum. Pick any two ideals $(x-\sigma(\zeta_p))$ and $(x-\sigma'(\zeta_p))$. Then $\sigma(\zeta_p)-\sigma'(\zeta_p)$ will be in the sum ideal. This is a difference of two distinct powers of $\zeta_p$, so generates the same ideal as one of the $1-\zeta_p^k$, $0<k<p$.
probability - Showing that $ {\rm E} [X]=\sum_ {k=0}^\infty P (X>k ...
The sum of the first column will be $$\sum_{k=1}^{\infty}\mathbb P(X=k)=\mathbb P(X>0).$$ The sum of the second column will be $$\sum_{k=2}^{\infty}\mathbb P(X=k)=\mathbb P(X>1).$$ The sum of the third column will be $$\sum_{k=3}^{\infty}\mathbb P(X=k)=\mathbb P(X>2)$$ and so …
Calculate $\\sum_{k=0}^n k \\binom{n}{k} p^k (1-p)^{n-k}$
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Let $G$ be a group and $a\\in G$ have order $k$. If $x^p=a$, …
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Let $n \\in \\mathbb{N}$ for all $k \\in \\{1,2...,n\\}$ and …
2017年10月13日 · To answer the questions, you really need to utilize the linearly independence of $\{ 1, x, x^2, \cdots, x^n \}$, induction should work just fine for (i). For part (ii), again the argument follows through an induction manner.