Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 205

2010 USAMO #5:Prove that if $frac{1}{p}-2S_q = frac{m}{n}$ for integers $m$ and $n$, then $m - n$ is divisible by $p$.

Let $q = frac{3p-5}{2}$ where $p$ is an odd prime, and let $S_q = frac{1}{2cdot 3 cdot 4} + frac{1}{5cdot 6 cdot 7} + cdots + frac{1}{q(q+1)(q+2)}...

Asked on 09/07/2020 by Shubhangi

2 answer

Frechet derivative limit

I was solving a problem by using the Frechet derivative to find the maximum. I result to the following limit $$lim_{||x||_{mathbb{L}^2}to 0}frac{|f(x+t)-f(t)-J_{f(t)}(x)|_{mathbb{R}}}{||x||_{mathbb{L}^2}}=...=underbrace{lim_{||x||_{mathbb{L}^2}to 0}frac{|mathbb{E}(x^2)|_{mathbb{R}}}{||x||_{mathbb{L}^2}}}_{text{why is this equal to $||x||_{mathbb{L}^2}$}}=||x||_{mathbb{L}^2}to 0$$...

Asked on 09/07/2020 by Nav89

0 answer

If $m^*(Acap(a,b))leqfrac{b-a}{2}$. Show that $m(A)=0$.

Let $Asubsetmathbb{R}$ such that $m^*(Acap(a,b))leqfrac{b-a}{2}$ for any $a,binmathbb{R}$. Show that $A$ is measurable and $m(A)=0$.Here $m^*(A)$ is the Lebesgue outer measure of ...

Asked on 09/06/2020 by gune

2 answer

Which theorems and definitions do I need to know to prove the impossible chessboard puzzle has a solution for every number of squares?

I saw this problem on the youtube channel called 3blue1brown. The problem is the following: There is a 8 x 8 chessboard, two prisoners (Prisoner 1 and prisoner 2), a...

Asked on 09/04/2020 by bob_the_fat

0 answer

Prove that $sqrt{x} > ln x$ for all $x>0$ with a study of function

Prove that for all $x>0$ it is $sqrt{x} > ln x$. I've defined the function $D(x)=sqrt{x}-ln x$, I've studied its first derivative and I've concluded that ...

Asked on 09/01/2020 by ZaWarudo

4 answer

Radical of ideal: Radical of $4mathbb Z = 2mathbb Z$?

The definition says that $x^n$ is in the ideal but I don't see what positive integer $4$ can be raised to in order to get $2$....

Asked on 08/31/2020 by dabofskateboarding

3 answer

Finding principal curvatures at points on a surface without parametrization

I have some points in 3D space. I can fit the equation of a surface z = f(x,y) to them either globally or locally.However:The surface does not pass through...

Asked on 08/31/2020 by confusedstudent

1 answer

Books for beginners on the Fourier Transform

I am a student who has just finished high school. I can easily handle IB level differentiation, integration and complex numbers. I am interested in learning about the Fourier Transform....

Asked on 08/30/2020 by user10764803

2 answer

Example of a cocommutative, non-unimodular Hopf algebra?

1. Definitions: Unimodularity and cocommutativityLet $H$ be a Hopf algebra over a field $mathbb k$.We call $H$ unimodular if the space of left integrals $I_l(H)$...

Asked on 08/30/2020 by M.C.

1 answer

Can we determine if $y(x)=frac {c-x}{x+1}$ has any strictly positive integer solutions?

The equation is as follows: $$y=frac {c-x}{x+1}$$ Where $c$ is a positive, even integer. Is it possible to determine whether there are any positive integer solutions different than...

Asked on 08/28/2020 by Estagon

3 answer

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