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New posts in polynomials
How often must an irreducible polynomial take a prime value?
number-theory
polynomials
prime-numbers
Prove that $e$ is transcendental.
real-analysis
calculus
proof-verification
polynomials
transcendental-numbers
If $\alpha$ is an algebraic element and $L$ a field, does the polynomial ring $L[\alpha]$ is also a field?
polynomials
field-theory
extension-field
$x^n - a$ is irreducible over $\mathbb{Q}$?
polynomials
irreducible-polynomials
How to prove that all zeros of the complex polynomial $P(z)$ lie in $\Bbb{D}$?
complex-analysis
polynomials
roots
complex-geometry
Coeff. of $x^{97}$ in $f(x) = (x-1)\cdot (x-2)\cdot (x-3)\cdot (x-4)\cdot ........(x-100)$
algebra-precalculus
polynomials
sums-of-squares
multinomial-coefficients
Are quartic minimal polynomials over $\mathbb{Q}$ always reducible over $\mathbb{F}_p$?
polynomials
galois-theory
finite-fields
Prime numbers which divide $n^3-3n+1$
number-theory
polynomials
prime-numbers
GCD of $n^a\,\prod\limits_{i=1}^k\,\left(n^{b_i}-n\right)$ for $n\in\mathbb{Z}$
number-theory
polynomials
prime-numbers
prime-factorization
When does a system of polynomial equations have infinitely many solutions?
abstract-algebra
algebraic-geometry
polynomials
systems-of-equations
computer-algebra-systems
Different ways to factor
polynomials
soft-question
factoring
Given an integer, how can I detect the nearest integer perfect power efficiently?
number-theory
polynomials
algebraic-number-theory
exponentiation
perfect-powers
Infinitely many solutions leads to existence of a polynomial
number-theory
polynomials
arithmetic-geometry
Prove that a polynomial of degree $d$ has at most $d$ roots (without induction)
abstract-algebra
polynomials
field-theory
Proving (without using complex numbers) that a real polynomial has a quadratic factor
abstract-algebra
polynomials
real-numbers
alternative-proof
For positive real numbers $a,b$ prove that $\sqrt[3]{2(a+b)(\frac{1}{a}+\frac{1}{b})}\ge\sqrt[3]{\frac{a}{b}}+\sqrt[3]{\frac{b}{a}}$.
algebra-precalculus
inequality
polynomials
means
a.m.-g.m.-inequality
How can you tell if a least squares/rootfinding problem is well conditioned only by calculating the roots of a polynomial fit?
polynomials
numerical-methods
numerical-linear-algebra
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
number-theory
polynomials
ring-theory
Solving $45x-3795x^3 +95634x^5 - \cdots + 945x^{41}-45x^{43}+x^{45} = N$?
algebra-precalculus
trigonometry
polynomials
What are the factors of this quotient given by Fermat's Little Theorem?
elementary-number-theory
polynomials
irreducible-polynomials
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