query: Prove every finite field is of cardinality $p^n$
positive_passages.docid: 55894
positive_passages.text: Is there anything like GF(6)?
negative_passages.docid: 47091
negative_passages.text: How to construct finite fields of any prime power order?
negative_passages.docid: 41661
negative_passages.text: Show that the set of all finite subsets of $\mathbb{N}$ is countable.
negative_passages.docid: 23712
negative_passages.text: $F$ is a finite field of size $s$. Prove that if $s=2^m$ for some $m>0$, then all elements of F have a square root.
negative_passages.docid: 10885
negative_passages.text: Existence of irreducible polynomials over finite field
negative_passages.docid: 23526
negative_passages.text: Complexity of arithmetic in a finite field?
negative_passages.docid: 62687
negative_passages.text: Proving Cardinality of Cosets in Abstract Algebra
negative_passages.docid: 51770
negative_passages.text: Number of elements in a finite field extension for finite fields
negative_passages.docid: 86421
negative_passages.text: Proof of the definition of cardinal exponentiation
negative_passages.docid: 74777
negative_passages.text: Solvability and reducibility of a polynomial in a "chain" of finite fields
negative_passages.docid: 127200
negative_passages.text: Are there fields and ordered fields of every infinite cardinality?
negative_passages.docid: 42677
negative_passages.text: Proving $(\alpha + \beta)^{p^n} = \alpha^{p^n} + \beta^{p^n}$ in a finite field
negative_passages.docid: 132133
negative_passages.text: Number of elements of a finite field
negative_passages.docid: 101669
negative_passages.text: Cardinality of the Set of all finite subset of $\mathbb{R}$
negative_passages.docid: 24403
negative_passages.text: Prove that $ n < 2^{n}$ for all natural numbers $n$.
negative_passages.docid: 128437
negative_passages.text: How to prove that a finite set is countable
negative_passages.docid: 25685
negative_passages.text: What is the product of all nonzero, finite cardinals?