A common formulation of the Chinese remainder theorem (CRT) is as follows: Let (m_{1}, ldots, m_{k}) be

Question:

A common formulation of the Chinese remainder theorem (CRT) is as follows: Let $m_{1}, \ldots, m_{k}$ be integers that are pairwise relatively prime for $1 \leq i, j \leq k$, and $i eq j$. Define $M$ to be the product of all the $m_{i}{ }^{\prime}$ s. Let $a_{1}, \ldots, a_{k}$ be integers. Then the set of congruences:

image text in transcribed