Home/Algebra/Modular arithmetic/Chinese remainder theorem26. Modular arithmeticChinese remainder theoremLevel: avanzadoIn 26. Modular arithmeticFormulaCopy LaTeXx≡ai(modni);N=∏inix\equiv a_i\pmod{n_i};\quad N=\prod_i n_ix≡ai(modni);N=i∏niTagsalgebraarithmetic modularCSalgebra formulamodularDetailSystems with pairwise coprime moduli have a unique solution modulo N.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 section