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List the elements of the field $K = \mathbb{Z}_2[x]/f(x)$ where $f(x)=x^5+x^4+1$ and is irreducible

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#abstract-algebra #field-theory #finite-fields
163
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A count involving number of subspaces

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#finite-fields
101
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Why are these curves' points called rational?

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#algebraic-geometry #finite-fields
113
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Prove that the coefficients of a polynomial are in a finite field

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#field-theory #galois-theory #finite-fields
252
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Some questions on elliptic curves over finite fields

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#finite-fields #elliptic-curves
740
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Existence of ring homomorphism from $\mathbb{Z}[\frac{i}{2}]$ to a finite field

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#abstract-algebra #number-theory #ring-theory #finite-fields #ring-homomorphism
1.6k
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Is finding generators of finite fields hard?

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#abstract-algebra #number-theory #finite-fields #computational-complexity
537
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How does one construct the Galois field extension $GF((2^2)^3)$?

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#field-theory #galois-theory #finite-fields #extension-field
307
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Polynomials over a finite field

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#abstract-algebra #polynomials #field-theory #finite-fields
1.1k
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Sum of powers in finite fields

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#finite-fields
1.2k
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Proof that algebraically closed fields of characteristic $p$ exist

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#abstract-algebra #finite-fields
110
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List all elements in the residue field $Z[i]/(q)$

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#number-theory #prime-numbers #algebraic-number-theory #finite-fields
995
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Modular curves over finite fields

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#algebraic-geometry #reference-request #finite-fields #elliptic-curves #modular-forms
204
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What is the exponent in the definition of a Galois field called?

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#finite-fields
386
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How does the multiplicative group of a finite field, considered as a vector space, act on subspaces?

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#finite-fields #projective-geometry #grassmannian #combinatorial-designs

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