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4
votes
0answers
1k views

how to solve this multivariate quadratic equation?

This has been posted on math.stackexchange but got just one partial(insightful though) comment. I'm posting it here in a hope of getting further ideas and comments: The problem was: Any hope to ...
3
votes
0answers
190 views

How to handle a polynomial whose roots exhibit obvious symmetry

I've got a sequence of polynomials, and for each of them the roots obviously follow a definite pattern. Here are the roots of the 34th one All others have their roots arranged in a similar ...
2
votes
0answers
421 views

System of two variables quadratic equations

Let $\mathcal{P}_{2,Z}$ be the set of all 2 variables quadratic equations $P(x,y)$ with integral coefficients: $$P(x,y)=a_1x^2+a_2y^2+a_3xy+a_4x+a_5y+a_6\ \ \ \ \ \ (a_i\in \mathbb{Z})$$ Consider a ...
1
vote
0answers
46 views

About the rank of a Pell equation-related matrix

I have a question about the solution of Pell-equation over a prime field. I want prove that the matrix $M$ is of rank $\frac{p-1}{2}$, with $M=(m_{i,j})\in\left(\mathbb{Z}/(p^p-1)\mathbb{Z} ...
1
vote
0answers
209 views

An equation about generating functions and subfactorial

As I promised, I clone the problem from Math.SE to here, in order to find a solution. Suppose $G_n(w)$ is a formal power series (really a probability generating function, see the following ...
1
vote
0answers
130 views

satisfiable polynomial equations for given free coefficients

Let $F$ be a finite field, $n, k, m$ be natural numbers. I give you $m$ vectors $c^{(1)},\ldots,c^{(m)}\in F^n$. I ask for polynomials $p_1,\ldots,p_n$ on $k$ variables over $F$ such that the system ...
0
votes
0answers
29 views

Does this system have a closed-form solution? $x_j = \left(\sum_{i=1}^n B_{ij} x_i\right)^\alpha $

I am interested in solving the following system of $n$ equations: $$x_j = \left(\sum_{i=1}^n B_{ij} x_i\right)^\alpha $$ for all $j\in\{1,\dots,n\}$, where $n$ is a positive integer, ...
0
votes
0answers
127 views

Random variables related through nonlinear system of equations

I asked this question on http://math.stackexchange.com/questions/377140/random-variables-related-through-nonlinear-system-of-equations, however I received no answer for a while so I'm posting it here: ...
0
votes
0answers
240 views

solving in x involving both exponential and logarithmic function

Is it possible to solve a function with both exponential and logarithm such as $a x^2 - b.\log(x) = c $ in closed form; where $a,b,c$ are constants and $a>0$ and $b>0$?