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I've been working on this problem, and I think that I almost have the solution, but I'm not quite there.Suppose that $A in M_n(mathbb C)$ has $n$ distinct...
Asked on 12/23/2021 by 100001
1 answerIn a club election the number of contestants is one more than the number of maximum candidates for which a voter can vote. If the total number of ways is...
Asked on 12/23/2021
2 answerIt's a try to find a closed form to the minimum of the function :Let $0<x<1$ then define :$$g(x)=x^{2(1-x)}+(1-x)^{2x}$$Denotes $x_0$ the abscissa of the...
Asked on 12/23/2021
2 answerThe question is from the pg - 59 from ' An Introduction to Diophantine Equations ' by Titu Andreescu , Dorin Andrica , Ion Cucurezeanu.Example 1 : Solve in positive...
Asked on 12/23/2021 by The Demonix _ Hermit
2 answerI am trying to prove that in $mathbb{Z}[sqrt{-1}]$, every non-unit divisor of $s+sqrt{-1}$ is not associate with an element of $mathbb{Z}$ (which means, it is not a...
Asked on 12/23/2021
2 answerSuppose $z$ and $omega$ are two complex numbers such that $|z|≤1$ and $|omega|≤1$ and $|z+iomega|=|z-iomega|=2$. Find $|z|$ and $|omega|$. My attempt: I squared...
Asked on 12/23/2021
3 answerLet $X$ be a real closed field. Let us define a constructible hierarchy relative to $X$ is defined as follows. (This is slightly nonstandard terminology.). Let...
Asked on 12/23/2021
1 answerOriginal question: Let A and B be two points lying on opposite sides of a given line l. Find all point(s) X on l such that |AX − BX| is...
Asked on 12/23/2021 by Vibhu Kapadia
1 answerSo I'm trying to solve this problem (which has some physics elements but it's mostly a math problem, I think). Here it is:Consider the image below: ...
Asked on 12/23/2021
1 answerHow does $$left(1+frac{x}{j}right)^{-1}left(1+frac{1}{j}right)^x=1+frac{x(x-1)}{2j^2}+Oleft(frac{1}{j^3}right)$$my attempt: It looks like maybe the taylor series of the numerator at 1 times the geometric of the denominator: $(1-(frac{x}{j})+(frac{x}{j})^2dots)(1+(1+1/j)^x(ln(1+1/j))(x-1)$ which obviously isn't the...
Asked on 12/23/2021
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