query: Finding the number of irreducible quadratics in $\Bbb Z_p[x]$, where $p$ is a prime
positive_passages.docid: 154373
positive_passages.text: How many irreducible monic quadratic polynomials are there in $\mathbb{F}_p[X]$?
negative_passages.docid: 53669
negative_passages.text: Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
negative_passages.docid: 78549
negative_passages.text: Any prime is irreducible
negative_passages.docid: 87289
negative_passages.text: Find the multiplicative inverses of all the elements in $\Bbb Z_{16}^\times$
negative_passages.docid: 144928
negative_passages.text: Find all primes $p$ such that $\phi(x)=x^{13}$ is a homomorphism $\Bbb Z/p\Bbb Z \rightarrow \Bbb Z/p\Bbb Z$.
negative_passages.docid: 90144
negative_passages.text: Show that if $a+bi$ is irreducible over $\mathbb{Z} [i]$ then $a^2 + b^2$ is prime over $\mathbb{Z} $
negative_passages.docid: 158182
negative_passages.text: Let $R = \mathbb{Z} + x\mathbb{Q}[x]$. Find all the irreducibles in $R$.
negative_passages.docid: 153062
negative_passages.text: Question about irreducible Gaussian integers
negative_passages.docid: 93196
negative_passages.text: $x^4 -10x^2 +1 $ is irreducible over $\mathbb Q$
negative_passages.docid: 26069
negative_passages.text: Why is $X^4-16X^2+4$ irreducible in $\mathbb{Q}[X]$?
negative_passages.docid: 108767
negative_passages.text: Irreducible Components of the Prime Spectrum of a Quotient Ring and Primary Decomposition
negative_passages.docid: 141124
negative_passages.text: Automorphisms of the ring $\Bbb Z[x]$ of polynomials with integer coefficients
negative_passages.docid: 15000
negative_passages.text: Show that number of elements in $(Z/nZ)^*$ is $\phi (n)$
negative_passages.docid: 79564
negative_passages.text: Algorithm to find the irreducible polynomial
negative_passages.docid: 140808
negative_passages.text: Problem on Galois theory and irreducible polynomial
negative_passages.docid: 153647
negative_passages.text: Elementary number theory and quadratic
negative_passages.docid: 87101
negative_passages.text: Irreducible but not prime in $K[X,Y]/(X^2-Y^3)$