6. Chinese Remainder Theorem

Constructive Solutions — Quiz

Test your understanding of constructive solutions with 5 practice questions.

Practice Questions

Question 1

What is the least nonnegative integer $x$ such that $x \equiv 2 \pmod{3}$ and $x \equiv 3 \pmod{5}$?

Question 2

What is the least nonnegative integer $x$ such that $x \equiv 1 \pmod{4}$ and $x \equiv 2 \pmod{5}$?

Question 3

What is the modular inverse of $3$ modulo $7$?

Question 4

If the moduli are $4$ and $9$, what is the modulus of the unique combined solution in the Chinese Remainder Theorem?

Question 5

In the constructive method for two coprime moduli, if $M = m_1 m_2$, what is $M_1 = \frac{M}{m_1}$?