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The 51 pages that link to Finite field, each with the reason it gives.

• Incidence geometryRelated: Incidence questions over finite fields have algebraic constraints and bounds distinct from real geometry.

• André WeilRelated: Counting points over finite fields is central to the results bearing Weil’s name.

• Finite setRelated: Its underlying finite set supports algebraic operations used in coding and cryptography.

• Root of unityRelated: Roots of unity in finite fields support transforms and cyclic multiplicative subgroups.

• Cyclotomic polynomialRelated: Reducing cyclotomic polynomials modulo primes helps study roots of unity in finite fields.

• Galois theoryRelated: Its extensions have explicitly describable cyclic Galois groups generated by Frobenius.

• Quotient ringRelated: Quotienting a polynomial ring by an irreducible polynomial can produce one.

• Splitting fieldRelated: Splitting fields of polynomials over finite fields are finite fields.

• Legendre symbolRelated: Residue classes modulo p form the finite field in which quadratic solvability is tested.

• Schur's theoremRelated: Schur used finite-field arithmetic to connect hypothetical Fermat solutions with a monochromatic sum.

• Euler's criterionRelated: The theorem's arithmetic takes place in the field of residues modulo p.

• Finite cyclic groupRelated: The nonzero elements of every finite field form a cyclic group under multiplication.

• Finite geometryRelated: Vector spaces over finite fields provide standard coordinates for finite geometries.

• Arithmetic geometryRelated: Counting solutions over finite fields often reveals information about varieties over number fields.

• Cauchy–Davenport theoremRelated: The residues modulo a prime form the field in which the theorem operates.

• Singleton boundRelated: Linear codes commonly use finite fields as their alphabets.

• Wedderburn's little theoremRelated: The established theory of finite fields provides the theorem's destination and context.

• Elwyn BerlekampRelated: Finite-field arithmetic underlies the algebraic codes Berlekamp helped design and decode.

• Hamming boundRelated: The alphabet size sets the number of words in the ambient space being packed.

• Mutually orthogonal Latin squaresRelated: Arithmetic in finite fields constructs large families of mutually orthogonal squares.

• Adi ShamirRelated: Secret-sharing arithmetic is performed over a finite field to keep shares bounded and exact.

• Agrawal's conjectureRelated: For prime n, residues modulo n form a field, underlying the identity's behavior.

• Ax–Grothendieck theoremRelated: Finite-field reductions turn injectivity into surjectivity for point sets.