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Test your understanding with targeted questions related to the topic.
Question 1
Easy
Solve the linear congruence 4x ≡ 2 (mod 10).
💡 Hint: Try dividing both sides if GCD of coefficients is 1.
Question 2
Easy
What is the multiplicative inverse of 3 mod 7?
💡 Hint: Find a number which, when multiplied by 3, gives a remainder of 1 when divided by 7.
Practice 4 more questions and get performance evaluation
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does the term 'linear congruence' refer to?
💡 Hint: Think about the context of modular operations.
Question 2
True or False: The Chinese Remainder Theorem guarantees a unique solution modulo the product of the pairwise co-prime moduli.
💡 Hint: Recall the main properties of CRT.
Solve 2 more questions and get performance evaluation
Push your limits with challenges.
Question 1
Prove that the solutions for the linear congruence 12x ≡ 12 (mod 18) include infinite entries.
💡 Hint: How can you express x based on multiples of the reduced expression?
Question 2
Given three congruences x ≡ 4 (mod 7), x ≡ 5 (mod 9), and x ≡ 6 (mod 10), find the smallest x that satisfies them.
💡 Hint: Combine each congruence carefully, noting pairwise properties.
Challenge and get performance evaluation