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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the solution to 2x ≡ 4 (mod 3)?
💡 Hint: Find the integer value of `x` satisfying the equation.
Question 2
Easy
Determine if 1x ≡ 5 (mod 10) has solutions, and if so, provide one.
💡 Hint: Solve the equation normally then check for modulo.
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 kind of equations are expressed as ax ≡ b (mod N)?
- Linear equations
- Linear Congruences
- Quadratic equations
💡 Hint: Look for terms that involve modulus.
Question 2
True or False: Every linear congruence has at least one solution.
- True
- False
💡 Hint: Consider the structure of congruences.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that if ax ≡ b (mod N) has a solution for GCD(a, N) = d, then it implies a system of equations.
💡 Hint: Use properties of divisors and modular arithmetic.
Question 2
For three congruences x ≡ 1 (mod 6), x ≡ 2 (mod 15), and x ≡ 3 (mod 10), find all solutions up to M.
💡 Hint: Work through each congruence step to consolidate solutions.
Challenge and get performance evaluation