Chinese theorem

Returns the solution of the system of equations given by the Chinese theorem: let $n_1,...,n_k$ be integers greater than 1, and let us denote by $N$ the product of the $n_i$. The Chinese remainder theorem states that if the $n_i$ are pairwise coprime, and if $a_1,...,a_k$ are any integer, $0\le a_i<n_i$, then there exists an integer $x$ such that

$\begin{array}{c}x\equiv a_1(\text{mod}{n}_1)\\ ⋮\\ x\equiv a_k(\text{mod}{n}_k)\end{array}$

and two such $x$ are congruent modulo $N$.

chinese_theorem(Integer, Integer, Integer, Integer)

chinese_theorem(List, List)

Description

Given four integers $a_1$, $a_2$, $n_1$, $n_2$, returns $x$, the solution of the system of equations described above.

Given two lists $\{a_1,...,a_k\}$ and $\{n_1,...,n_k\}$, returns $x$, the solution of the system of equations described above.