All Questions

Currently I'm stuck as follows; at least a positive proof if $n=3$ would be a great nice-to-have! Consider real numbers $x_1,x_2,\dots,x_n$ satisfying $$\prod^n_{k=1}\left(1-x_k^2\right)\:=\:\...

Is there a positive constant $K>0$ such that for every polynomials $f_1,\dots,f_4 \in\mathbb{Z}[X]$ with coefficients in {-1,0,1}, every positive root $x$ of the polynomial $$g=f_1f_2-f_3f_4$$ ...

I'm trying to find upper and lower bounds of the smallest positive root of a polynomial, stated in terms of its coefficients. As I appreciate it might be a very general problem, My specific interest ...

I'm interested in the question of given a differentiable and bounded function $f(\vec{x})$ (over a single variable or multiple variables, over a bounded domain $D$), finding a pair of polynomials $p_1(...

Let $f$ be a monic polynomial with bounded integer coefficients and such that all zeros are (in absolute value) greater than $1$. How close can the zeros of $f$ reach $1$ (in absolute value)? More ...