query: Find monic irreducible polynomial in p-field
positive_passages.docid: 12166
positive_passages.text: How many irreducible polynomials of degree $n$ exist over $\mathbb{F}_p$?
negative_passages.docid: 155559
negative_passages.text: Quickest way to determine a polynomial with positive integer coefficients
negative_passages.docid: 7954
negative_passages.text: Roots of monic polynomial over a number ring
negative_passages.docid: 106914
negative_passages.text: Existence of Irreducible polynomials over $\mathbb{Z}$ of any given degree
negative_passages.docid: 60816
negative_passages.text: Irreducibility of special cyclotomic polynomial.
negative_passages.docid: 100573
negative_passages.text: Show that $x^4-10x^2+1$ is irreducible over $\mathbb{Q}$
negative_passages.docid: 35959
negative_passages.text: irreducibility of a polynomial over $\mathbb{F}_2$
negative_passages.docid: 146591
negative_passages.text: Inseparable polynomial over a non-perfect field
negative_passages.docid: 40994
negative_passages.text: How to check that a cubic polynomial is irreducible?
negative_passages.docid: 121301
negative_passages.text: What are the roots of an irreducible $p\in F[X]$ in the field extension $F[X]/\langle p\rangle$?
negative_passages.docid: 76327
negative_passages.text: Finding inverse of polynomial in a field
negative_passages.docid: 154360
negative_passages.text: Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
negative_passages.docid: 44878
negative_passages.text: Factor $x^5+x^2+1$ into irreducible polynomials in $Z[x]$
negative_passages.docid: 93291
negative_passages.text: Method for determining irreducibles and factorising in $\mathbb Z[\sqrt{d}]$
negative_passages.docid: 137669
negative_passages.text: $P$ is a monic polynomial of degree $n$ , then which are correct?
negative_passages.docid: 54192
negative_passages.text: Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
negative_passages.docid: 155642
negative_passages.text: Understanding divison by monic polynomial in $R[x]$ where $R$ is an arbitrary ring