New posts in polynomials

How often must an irreducible polynomial take a prime value?

Prove that $e$ is transcendental.

If $\alpha$ is an algebraic element and $L$ a field, does the polynomial ring $L[\alpha]$ is also a field?

$x^n - a$ is irreducible over $\mathbb{Q}$?

How to prove that all zeros of the complex polynomial $P(z)$ lie in $\Bbb{D}$?

Coeff. of $x^{97}$ in $f(x) = (x-1)\cdot (x-2)\cdot (x-3)\cdot (x-4)\cdot ........(x-100)$

Are quartic minimal polynomials over $\mathbb{Q}$ always reducible over $\mathbb{F}_p$?

Prime numbers which divide $n^3-3n+1$

GCD of $n^a\,\prod\limits_{i=1}^k\,\left(n^{b_i}-n\right)$ for $n\in\mathbb{Z}$

When does a system of polynomial equations have infinitely many solutions?

Different ways to factor

Given an integer, how can I detect the nearest integer perfect power efficiently?

Infinitely many solutions leads to existence of a polynomial

Prove that a polynomial of degree $d$ has at most $d$ roots (without induction)

Proving (without using complex numbers) that a real polynomial has a quadratic factor

For positive real numbers $a,b$ prove that $\sqrt[3]{2(a+b)(\frac{1}{a}+\frac{1}{b})}\ge\sqrt[3]{\frac{a}{b}}+\sqrt[3]{\frac{b}{a}}$.

How can you tell if a least squares/rootfinding problem is well conditioned only by calculating the roots of a polynomial fit?

On the cubic generalization $(a^3+b^3+c^3+d^3)(e^3+f^3+g^3+h^3 ) = v_1^3+v_2^3+v_3^3+v_4^3$ for the Euler four-square

Solving $45x-3795x^3 +95634x^5 - \cdots + 945x^{41}-45x^{43}+x^{45} = N$?

What are the factors of this quotient given by Fermat's Little Theorem?