List questions from finite-fields

Published on 04 Apr 2026 - 12:01

105

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I have to show this polynomial is irreducible.

Published on 04 Apr 2026 - 11:58

1.2k

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Suppose that $a$ and $b$ belong to a field of order $8$ and that $a^2 + ab + b^2 =0$ then $a=0$ and $b=0$ .

Published on 03 Apr 2015 - 2:47

110

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Equivalence of $\mathbb{F}_p$ and $\mathbb{Z}/p\mathbb{Z}$

Published on 03 Apr 2015 - 17:08

1.2k

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Greatest common divisor of polynomial in Finite Field(256), AES

Published on 05 Apr 2015 - 13:52

40

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What is the best known lower bound for: $\max_{2\leq i\leq p-1}(ord_n(i)) $?

Published on 06 Apr 2015 - 18:51

409

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Orthogonal matrices over GF(2^t) with the first column fixed

Published on 06 Apr 2015 - 19:35

297

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Generating elements of large group of units of a field.

Published on 01 Apr 2026 - 12:05

39

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Algebra: Field Theory Question

Published on 07 Apr 2015 - 7:23

121

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Find a ring homomorphism $\tau: \mathbb{F} \rightarrow \mathbb{F}$

Published on 23 Feb 2026 - 12:04

628

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hyperplanes in finite vector spaces

Published on 09 Apr 2015 - 2:58

96

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Extensions of fields and dimension

Published on 09 Apr 2015 - 17:00

404

Views

About Cayley graphs on finite fields.

Published on 26 Mar 2026 - 7:57

1.9k

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Prove that $F[x]/(f(x))$ has $q^n$ elements

Published on 09 Apr 2015 - 17:54

73

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Subset of numbers analogous to primitive polynomials over finite fields

Published on 09 Apr 2015 - 20:01

List Question

Determine with proof the number of monic irreducible polynomials of prime degree $p$ over $F$

I have to show this polynomial is irreducible.

Suppose that $a$ and $b$ belong to a field of order $8$ and that $a^2 + ab + b^2 =0$ then $a=0$ and $b=0$ .

Equivalence of $\mathbb{F}_p$ and $\mathbb{Z}/p\mathbb{Z}$

Greatest common divisor of polynomial in Finite Field(256), AES

What is the best known lower bound for: $\max_{2\leq i\leq p-1}(ord_n(i)) $?

Orthogonal matrices over GF(2^t) with the first column fixed

Generating elements of large group of units of a field.

Algebra: Field Theory Question

Find a ring homomorphism $\tau: \mathbb{F} \rightarrow \mathbb{F}$

hyperplanes in finite vector spaces

Extensions of fields and dimension

About Cayley graphs on finite fields.

Prove that $F[x]/(f(x))$ has $q^n$ elements

Subset of numbers analogous to primitive polynomials over finite fields

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