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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the solution for x in 5x ≡ 15 (mod 10)?
💡 Hint: Check numbers that give a remainder of 5 when multiplied by 5.
Question 2
Easy
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.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What method do we use to solve ax ≡ b (mod N) confidently?
- A. Simple division
- B. Extended Euclid's Algorithm
- C. Graphical method
💡 Hint: Think about which method guarantees the necessary inverse.
Question 2
True or false: The Chinese Remainder Theorem guarantees a unique solution to every set of congruences.
- True
- False
💡 Hint: Consider the conditions of the theorem.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation