6. Chinese Remainder Theorem

Applications — Quiz

Test your understanding of applications with 5 practice questions.

Practice Questions

Question 1

What is the smallest positive integer $n$ such that $n\equiv 2 \pmod{3}$, $n\equiv 3 \pmod{5}$, and $n\equiv 2 \pmod{7}$?

Question 2

What is the smallest positive integer $n$ such that $n\equiv 2 \pmod{3}$, $n\equiv 1 \pmod{4}$, and $n\equiv 3 \pmod{5}$?

Question 3

If $x\equiv 2 \pmod{3}$ and $x\equiv 4 \pmod{5}$, what is the smallest nonnegative value of $x$?

Question 4

What is the smallest positive integer $n$ such that $n\equiv 0 \pmod{4}$, $n\equiv 1 \pmod{5}$, and $n\equiv 2 \pmod{3}$?

Question 5

What is the smallest positive integer $n$ such that $n\equiv 1 \pmod{2}$, $n\equiv 2 \pmod{3}$, and $n\equiv 3 \pmod{4}$?