query: If $F$ is a finite field then $|F|=p^n$ for prime $p$ and some integer $n$
positive_passages.docid: 3703
positive_passages.text: Order of finite fields is $p^n$
negative_passages.docid: 84641
negative_passages.text: Infiniteness of set of primes such $f$ have root $\mod p$
negative_passages.docid: 132133
negative_passages.text: Number of elements of a finite field
negative_passages.docid: 76813
negative_passages.text: The ring $ℤ/nℤ$ is a field if and only if $n$ is prime
negative_passages.docid: 86626
negative_passages.text: Finite fields, existence of field of order $p^n$,proof help
negative_passages.docid: 33247
negative_passages.text: Does $f(0)=0$ and $\left|f^\prime(x)\right|\leq\left|f(x)\right|$ imply $f(x)=0$?
negative_passages.docid: 66851
negative_passages.text: If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
negative_passages.docid: 7899
negative_passages.text: Show that if $p$ is prime then $\Bbb Z_p$ is a field
negative_passages.docid: 23526
negative_passages.text: Complexity of arithmetic in a finite field?
negative_passages.docid: 106401
negative_passages.text: Prove: $p-mq | f(m)$ where $m$ is any integer
negative_passages.docid: 36087
negative_passages.text: Every Function in a Finite Field is a Polynomial Function
negative_passages.docid: 126808
negative_passages.text: Is it true that if $f(x)$ has a linear factor over $\mathbb{F}_p$ for every prime $p$, then $f(x)$ is reducible over $\mathbb{Q}$?
negative_passages.docid: 120147
negative_passages.text: For what prime numbers $p$ is $x^2+x+1$ irreducible in $\mathbb{F}_p[X]$
negative_passages.docid: 141418
negative_passages.text: When is $\mathbb{F}_p[x]/(x^2-2)\simeq\mathbb{F}_p[x]/(x^2-3)$ for small primes?
negative_passages.docid: 115449
negative_passages.text: Inclusion of Fields whose order is a prime power
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: 10627
negative_passages.text: When is $X^n-a$ is irreducible over F?