Practice Proof Of Fermat's Little Theorem (12.1.4) - Introduction to Fermat’s Little Theorem and Primality Testing

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6 sample questions

Question 1.
State Fermat's Little Theorem in your own words.
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Think about what happens when you take a large exponent!
Question 2.
What does it mean for two numbers to be co-prime?
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Consider examples of small integers!
3Question 3.
What does Fermat's Little Theorem state?
- a^(p) ≡ 1 mod p
- a^(p-1) ≡ 1 mod p
- a^(p+1) ≡ 0 mod p
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Focus on what happens when a is raised to the power of p-1.
4Question 4.
True or False: All pseudo primes satisfy Fermat's little theorem for every base.
- True
- False
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Reflect on the nature of Carmichael numbers.
Question 5.
Prove that 13 is a prime using Fermat's Little Theorem.
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Use several examples of a and compute explicitly.
Question 6.
Find a Carmichael number greater than 561.
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Check divisibility and apply Fermat's theorem multiple times!

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