13.5 - Multiplication Modulo k
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Practice Questions
Test your understanding with targeted questions
What is the identity element in multiplication modulo 7?
💡 Hint: Think about what number keeps others unchanged when you multiply.
List the co-prime integers with respect to 4.
💡 Hint: Consider what numbers have no common factors with 4.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a group?
💡 Hint: Recall the definition of a group we discussed.
True or False: The identity element in multiplication modulo k is always 0.
💡 Hint: Think about what multiplying any number by 0 results in.
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Challenge Problems
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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.
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.
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