6. Chinese Remainder Theorem

Statement And Proof — Quiz

Test your understanding of statement and proof with 5 practice questions.

Practice Questions

Question 1

In the standard Chinese Remainder Theorem, what condition on the moduli $m_1,\dots,m_k$ guarantees the result?

Question 2

What does it mean for the moduli $m_1,\dots,m_k$ to be pairwise coprime?

Question 3

What does the Chinese Remainder Theorem guarantee about a system of congruences with pairwise coprime moduli?

Question 4

In the constructive proof, what is usually defined as $M_i$ when $M=\prod_{j=1}^k m_j$?

Question 5

Why does an inverse of $M_i$ modulo $m_i$ exist in the proof?