Home/Algebra/Modular arithmetic/Modular congruence26. Modular arithmeticModular congruenceLevel: intermedioIn 26. Modular arithmeticFormulaCopy LaTeXa≡b(modn) ⟺ n∣(a−b)a\equiv b\pmod n\iff n\mid(a-b)a≡b(modn)⟺n∣(a−b)Tagsalgebraarithmetic modularCSalgebra formulamodularDetailDefines equality of remainders modulo n.Explore the ideaFound an error? Contact us.Related formulasRelatedModular operationsa≡b, c≡d(modn)⇒a+c≡b+d, ac≡bd(modn)a\equiv b,\;c\equiv d\pmod n\Rightarrow a+c\equiv b+d,\;ac\equiv bd\pmod na≡b,c≡d(modn)⇒a+c≡b+d,ac≡bd(modn)Open formulaOpen in sectionRelatedModular 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 section