Home/Algebra/Modular arithmetic/Modular operations26. Modular arithmeticModular operationsLevel: intermedioIn 26. Modular arithmeticFormulaCopy LaTeXa≡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)Tagsalgebraarithmetic modularCSalgebra formulamodularDetailCongruences are preserved under addition and multiplication.Explore the ideaFound an error? Contact us.Related formulasRelatedModular congruencea≡b(modn) ⟺ n∣(a−b)a\equiv b\pmod n\iff n\mid(a-b)a≡b(modn)⟺n∣(a−b)Open formulaOpen in sectionRelatedXORA⊕B=AˉB+ABˉA\oplus B=\bar AB+A\bar BA⊕B=AˉB+ABˉOpen formulaOpen in section