Home/Algebra/Algebraic structures/Prime finite field27. Algebraic structuresPrime finite fieldLevel: avanzadoIn 27. Algebraic structuresFormulaCopy LaTeXFp=Z/pZ(p primo)\mathbb F_p=\mathbb Z/p\mathbb Z\quad(p\text{ primo})Fp=Z/pZ(p primo)TagsalgebraCSstructuresstructures algebraicalgebra formulaDetailFundamental finite field in cryptography and coding theory.Explore the ideaFound an error? Contact us.Related formulasRelatedModular inverseaa−1≡1(modn) ⟺ gcd(a,n)=1aa^{-1}\equiv1\pmod n\iff\gcd(a,n)=1aa−1≡1(modn)⟺gcd(a,n)=1Open formulaOpen in sectionRelatedFermat's little theoremap−1≡1(modp)(p∤a)a^{p-1}\equiv1\pmod p\quad(p\nmid a)ap−1≡1(modp)(p∤a)Open formulaOpen in section