5. Linear Congruences

Solvability Conditions — Quiz

Test your understanding of solvability conditions with 5 practice questions.

Practice Questions

Question 1

Which condition must hold for the linear congruence $ax \equiv b \pmod n$ to have at least one solution?

Question 2

Which statement is correct about the congruence $8x \equiv 5 \pmod{12}$?

Question 3

If $\gcd(a,n)=1$, what can you say about the congruence $ax \equiv b \pmod n$ for any integer $b$?

Question 4

How many incongruent solutions does $4x \equiv 8 \pmod{12}$ have?

Question 5

Which congruence has no solution?