Practice Summary and References - 7.6 | 7. Lecture - 55: Modular Arithmetic | Discrete Mathematics - Vol 3
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Practice Questions

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Question 1

Easy

What is 9 modulo 4?

💡 Hint: Think of how many times 4 fits into 9.

Question 2

Easy

Is 8 congruent to 2 modulo 3?

💡 Hint: Calculate the remainder of both numbers when divided by 3.

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Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is the result of 14 modulo 5?

  • 2
  • 3
  • 4

💡 Hint: Think about how many times 5 fits into 14.

Question 2

True or False: Division is always well-defined in modular arithmetic.

  • True
  • False

💡 Hint: Consider cases where the divisor is congruent to zero.

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Challenge Problems

Push your limits with challenges.

Question 1

Using the square and multiply method, calculate 2^13 modulo 19 and explain each step.

💡 Hint: Make sure to convert the exponent to binary and track your calculations carefully.

Question 2

Why is it important for cryptographic algorithms to use modular exponentiation? Discuss with examples.

💡 Hint: Think about key generation and secure message transmission in cryptography.

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