Practice Discrete Mathematics (12.1) - Introduction to Fermat’s Little Theorem and Primality Testing

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6 sample questions

Question 1.
What is Fermat's Little Theorem?
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Think about the relationship between primes and powers.
Question 2.
State the corollary of Fermat's Little Theorem.
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Consider how division by p affects powers.
3Question 3.
What does Fermat's Little Theorem state?
- a^(p-1) ≡ 0 (mod p)
- a^(p-1) ≡ 1 (mod p)
- a ≡ 0 (mod p)
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Think about congruence relations with primes.
4Question 4.
True or False: Carmichael numbers pass Fermat's theorem condition for every base.
- True
- False
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Consider definitions of pseudo primes.
Question 5.
Demonstrate that 623 is not prime using Fermat’s theorem and explain the reasoning.
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Use several bases to test the true nature of 623.
Question 6.
Using Fermat’s theorem, test whether 341 can be declared prime given various bases and show examples.
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Check bases coprime with 341; recall 341 = 11 * 31.

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