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First let $N = p^2$. I think that to show that any number less than $N$ is prime, you only have to check to show it has factors...

2Mathematics Asked by Mondo Duke on 1 year ago

Here is part of Exercise 5.5.19 in Dummit & Foote's Abstract Algebra:Let $H$ be a group of order $n$, let $K=operatorname{Aut}(H)$ and $G=operatorname{Hol}(H)=Hrtimes K$ (where ...

1Mathematics Asked on 1 year ago

First question, do probability problems generally consisting of two categories always assume two events are dependent? Let's say there are two categories from a set of n people. They are...

0Mathematics Asked on 1 year ago

Let $Y$ be a connected normal Noetherian scheme, $f: Xto Y$ is an etale morphism of finite type. We assume $X$ is also connected. I have proved...

0Mathematics Asked on 1 year ago

For simplicity, I'll focus on the bivariate case. Let $(X_1,X_2)$ be a random vector that obeys bivariate Bernoulli. $X_i$ takes either zero or one. The associated pdf can...

1Mathematics Asked on 1 year ago

I'm looking for cases of invalid math operations producing (in spite of it all) correct results (aka "every math teacher's nightmare"). One example would be "cancelling" the 6's in ...

41Mathematics Asked on 1 year ago

Let$B = { mathbb{R} } cup { (a,b) capmathbb {Q} , alt b , a,b inmathbb{Q}}$ Thus, a set $V in B$...

1Mathematics Asked by roslavets on 1 year ago

I have a differential equation $X'=AX$ where $Ainmathcal M_n(Bbb R)$. The question is to prove that if all the solutions have a constant norm then $A$ is skew-symmetric matrix. What...

3Mathematics Asked by As soon as possible on 1 year ago

Let $sigma(x)$ denote the sum of divisors of the positive integer $x$. A number $y$ is said to be perfect if $sigma(y)=2y$. Denote the abundancy index...

1Mathematics Asked on 1 year ago

Question: Given Lebesgue integrable $f: mathbb{R}rightarrow [0,infty)$, prove the following series converges almost everywhere on $mathbb{R}$:$$varphi(x) = lim_{krightarrow infty} sum_{t=-k}^k f(t+x)$$ Attempt: Towards a contradiction suppose...

1Mathematics Asked by Christopher Rose on 1 year ago

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