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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the identity element in multiplication modulo 7?
💡 Hint: Think about what number keeps others unchanged when you multiply.
Question 2
Easy
List the co-prime integers with respect to 4.
💡 Hint: Consider what numbers have no common factors with 4.
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 group?
- A set with one operation
- A collection of elements that satisfies certain properties
- A number line
💡 Hint: Recall the definition of a group we discussed.
Question 2
True or False: The identity element in multiplication modulo k is always 0.
- True
- False
💡 Hint: Think about what multiplying any number by 0 results in.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that if a and b are in ℤ* for some k, then the inverse of their product in multiplication modulo k is the product of their inverses.
💡 Hint: Use the definition of inverses in group theory.
Question 2
Given k as a prime number, explain how ℤ* under multiplication modulo k simplifies to the entire non-zero set of integers less than k.
💡 Hint: Utilize the property of primes in relation to factors.
Challenge and get performance evaluation