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Finite fields, existence of field of order $p^n$,proof help

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#field-theory #finite-fields
1.4k
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Number of solutions to $x^2+y^2=1$ in a finite field?

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#abstract-algebra #finite-fields
164
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Factoring a polynomial over finite field $\,F_3$ that has a root

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#linear-algebra #polynomials #finite-fields
295
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Inverse of polynomial over $\mathbb F_3$ finite field, quotient space

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#polynomials #finite-fields #extension-field
102
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Find the number of 3 x 3 matrices with elements in $F_p$ such that determinant is non zero?

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#number-theory #finite-fields
617
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Symmetric groups and the "field with one element"

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#group-theory #intuition #finite-fields #symmetric-groups #algebraic-k-theory
862
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Subring of a matrix ring over a finite field?

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#abstract-algebra #matrices #finite-fields
191
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$x^5-1$ completely splits in $\mathbb F_{16}$

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#abstract-algebra #polynomials #field-theory #finite-fields
2.8k
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Ring structure on the Galois group of a finite field

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#abstract-algebra #ring-theory #field-theory #galois-theory #finite-fields
82
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Solving an equation in a field.

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#polynomials #finite-fields
694
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Weighted sum of squares, in a finite field

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#elementary-number-theory #finite-fields #square-numbers #sums-of-squares
361
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On the fields of rational fractions over $\mathbb{F}_{p}$

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#abstract-algebra #field-theory #galois-theory #finite-fields
74
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How to prove this well-known fact?

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#abstract-algebra #finite-fields
1.2k
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Algorithm to find solution to $ax^2 + by^2 = 1$ in a finite field

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#elementary-number-theory #finite-fields #square-numbers #sums-of-squares
423
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Is $\mathbb{Z}_p$ a Finite Field?

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#modular-arithmetic #finite-fields #equivalence-relations

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