# All Questions

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### Proove By Induction (Fibonacci Sequence)

Prove by PMI $\gcd(f_n,f_{n+1}) = 1$ for all natural numbers $n$. $f_n$ represents the Fibonacci sequence.
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### Complex integrations

Calculate integrals $$\oint_{|z|=1} \frac{z^2 e^z}{2z+i} dz$$ and $$\oint_{|z|=2} \frac{e^z}{z^2+z} dz$$ These are simple integrals to do with cauchy integral theorem right? First one. ...
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### Newton-Raphson with Exponentials

I'm having trouble getting initial values for x and y to be thrown into the Newton Raphson formulae, aka Xv1 and Yv1 respectively. Question; Show that the equation: 10e^-2x = 2x + 3x^2 has a root ...
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### Abstract Algebra and Chess

I am currently debtating to do a Mathmatics Paper on the comparison between the game of Chess and contemporary mathematics (namely group theory). I was wondering if this has potential to be a ...
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### MR Function Question

I have a question about MR Function below: P = 1/Q^2 + 3Q + 1 Find the MR Function and Evaluate it at Q = 4 Are you guys able to elaborate? I've never done these types of questions before, am i ...
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### What is the formula to generate this number sequence : 1 , 7 , 14, 30

What is the formula to generate this number sequence : 1 , 7 , 14, 30 I'm sure this is very simple for you guys. But it's got me alittle stuck. Thanks To clarify, I'm not an advanced maths student. ...
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### Are the normed spaces $\mathbb{R}^{n^2}$ and $M_n(\mathbb{R})$ isometric?

Consider the spaces $\mathbb{R}^{n^2}$ with euclidean norm and $M_n(\mathbb{R})$ of $n\times n$ matrices with the norm defined by $\Vert A\Vert = \sup\limits_{\Vert x\Vert \le 1}\Vert Ax\Vert$. ...
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### Connection between linear independence, non-/trivial and x solutions

I am having a hard time remembering which goes hand in hand with what. The math questions I get always include words like trivial etc. 1 solution no solution infinite amount of solutions And then ...
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### how to find if a number has a representation in a powerbase format?

I better explain this problem with an example, $100$ would be represented as $983$ because $9^1 + 8^2 + 3^3$ is one hundred. So how to find the relation between the number $n$ and numbers that can be ...
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### Solve in integers: $x^2 = y^2 + y + 1$

Solve this equation in integers: $$x^2 = y^2 + y + 1$$ I know $2$ ways to solve this. But they are not easy. Maybe there is some quick method.
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### Check if the angle is constructable

To check if an angle $x$ is constructable do we have to use the formula $\cos{3 \theta}=4\cos^3{\theta}-3\cos{\theta}$ and find the minimum irreducible polynomial that $\cos{x}$ satisfies and if its ...
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### How to show that the vertices of a convex hull are given by these specific subsets…

We work over $\mathbb{R}^N$. Let $V$ be the corners of the unit cube $[0,1]^N$, or equivalently the set of vectors whose coordinates take values $0$ or $1$. Let $d:\{0, \ldots, N\} \to \mathbb{R}_+$ ...
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### For any integer a, if $6|(3−a)$, then $3| (a−2)$.

Prove: For any integer a, if $6|(3−a)$, then $3| (a−2)$. I've been trying to work this problem for a while, but missed a day of class and can't seem to work it out.
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### Torsion free module over a PID is flat

Suppose a ring of integers $S$ is an extension of a ring of integers $R$ with $\mathfrak{q}$ a prime ideal in $S$ and $\mathfrak{p}=\mathfrak{q}^c$ in $R$. Is there a straightforward way of showing ...
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### Integral Contest

Before you answer this OP, please read all the terms and conditions below. Thank you... Today I hold an unofficial little contest on brilliant.org. Now, I will hold it here on Math S.E. It's just for ...
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### Inductive Property of Sets?

Why doesn't the set: ${2,4,6,8,10,.....}$ have the inductive property. For example $n = 2k$. So for every value of k you get a value of $n$. Plus $k+1$ is also present. So shouldn't this set have ...
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### Why have we made a function to be many to one and not one to many?

We have allowed function to only relate many to one but not one to many. Why haven't we included sin(x) to be a function? Is it just for simplicity? Also, I've seen someone quote a function not even ...
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### What is special about a transformation if the matrix of that transformation is symmetric?

If the matrix of a linear transformation T$\colon \mathbb{R}^{N} \rightarrow \mathbb{R}^{N}$ with respect to some basis is symmetric, what does it say about the transformation? Is there a way to ...
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### find the differential dy

I know this is right is it not? I did the work and I am almost positive I did it right.
I am currently working through an exercise set and I am a little stuck on the following question: For $a > 0$, define a function \$f_a(x)= \begin{cases} x^a \sin(1/x), &x \ne 0\\0, &x=0 ...