9H (source code)
= 9H
{scope}
{title2=Number Theory}
The <Chinese remainder theorem> says that for pairwise coprime positive moduli $n_i$, arbitrary residue classes modulo each $n_i$ specify one residue class modulo $\prod_i n_i$. For an odd positive integer $N=\prod p_i^{e_i}$, the <Jacobi symbol> is $(a/N)=\prod_i(a/p_i)^{e_i}$, where each factor is a <Legendre symbol>; for $N=1$ the empty product is one. The <Jacobi symbol> is multiplicative in $a$, and is zero exactly when $a$ and $N$ have a common prime factor.
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