\begin{definition}[Definition:Simultaneous Congruences]
A '''system of simultaneous congruences''' is a set of polynomial congruences:
:$\forall i \in \closedint 1 r: \map {P_i} x \equiv 0 \pmod {n_i}$
That is:
{{begin-eqn}}
{{eqn | l = \map {P_1} x
      | r = 0
      | rr= \pmod {n_1}
      | c = 
}}
{{eqn | l = \map {P_2} x
      | r = 0
      | rr= \pmod {n_2}
      | c = 
}}
{{eqn | o = \cdots
      | c = 
}}
{{eqn | l = \map {P_r} x
      | r = 0
      | rr= \pmod {n_r}
      | c = 
}}
{{end-eqn}}
\end{definition}