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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the form of a linear congruence?
💡 Hint: Look for the equation that involves a modulus.
Question 2
Easy
Can a linear congruence have infinitely many solutions?
💡 Hint: Consider the adjustments involving k.
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 is a linear congruence?
- A polynomial equation
- An equation in modular arithmetic
- A geometric representation
💡 Hint: Focus on the definition involving moduli.
Question 2
True or False: The Chinese Remainder Theorem assures a unique solution for any system of linear congruences.
- True
- False
💡 Hint: Consider the conditions under which CRT applies.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Find all integer solutions for the linear congruence \( 8x \equiv 16 \mod{48} \) and explain your steps.
💡 Hint: Consider how to simplify the equation.
Question 2
Prove that if \( a \) is a solution of the system of congruences from the Chinese Remainder Theorem, then any number of the form \( a + lm \) (where \( m \) is the product of modulus) is also a solution.
💡 Hint: Write out what happens for each modulus.
Challenge and get performance evaluation