10.7 - Construction of the Solution x
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What is the solution for x in 5x ≡ 15 (mod 10)?
💡 Hint: Check numbers that give a remainder of 5 when multiplied by 5.
If 3x ≡ 6 (mod 9), what are possible values for x?
💡 Hint: Look for x that, when multiplied by 3, gives a remainder of 6.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What method do we use to solve ax ≡ b (mod N) confidently?
💡 Hint: Think about which method guarantees the necessary inverse.
True or false: The Chinese Remainder Theorem guarantees a unique solution to every set of congruences.
💡 Hint: Consider the conditions of the theorem.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Solve the system of congruences using CRT:
- x ≡ 1 (mod 5)
- x ≡ 4 (mod 7)
- x ≡ 6 (mod 11).
💡 Hint: Think through each modulus contributions, expressing them individually.
Prove that if ax ≡ b (mod N) can be solved, then gcd(a, N) divides b.
💡 Hint: Consider the implications of solutions to mod forms.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.