List questions from irreducible-polynomials | MathQa

Understanding calculations of log/antilog tables of polynomials over finite field

Published on 12 Jan 2025 - 19:17

How do I show $x^2+1$ is reducible or irreducible in $\mathbb{Z}_7$?

Published on 12 Jan 2025 - 23:53

$a,b$ algebraic over $F$, $([F(a):F], [F(b):F]) = 1 \implies m_b(X)$ irreducible in $F(a)[X]$.

Published on 12 Jan 2025 - 23:48

Prove that $X^3+Y^3+X^2Y+XY^2+Y^2-Y$ is irreducible in $\mathbb{Z}[X,Y]$

Published on 12 Jan 2025 - 9:17

Factoring $x^3-3x-1\in \Bbb Q[x]$ in terms of a unknown root

Published on 12 Jan 2025 - 23:41

$(X^m-Y^n)$ is a prime ideal in $A[X,Y]$ iff $m, n$ are coprime

Published on 12 Jan 2025 - 9:17

Irreducibility of $f(x)=x^4-x^3+14x^2+5x+16$?

Published on 12 Jan 2025 - 23:55

Galois group. $K$-automorphisms take adjoined roots to other roots of minimal polynomial or take roots of $f$ to other roots of $f$

Published on 12 Jan 2025 - 23:40

Irreducible or reducible polynomials in $\mathbb Z_3[X]$ of degree 0,1,2,3

Published on 12 Jan 2025 - 9:17

Show these two polynomials are irreducible over $\mathbb{Q}$

Published on 12 Jan 2025 - 9:17