Practice Understanding Fermat's Little Theorem (12.2) - Introduction to Fermat’s Little Theorem and Primality Testing

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6 sample questions

Question 1.
State Fermat's Little Theorem.
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Recall the conditions regarding p and a.
Question 2.
What does it mean for two numbers to be co-prime?
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Think about the factors of the numbers.
3Question 3.
What does Fermat's Little Theorem state?
- a^(p-1) ≡ 0 (mod p)
- a^(p-1) ≡ 1 (mod p)
- a^(p) ≡ 1 (mod p)
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Think about the prime’s relation with its multiples.
4Question 4.
Carmichael numbers behave like primes under which condition?
- True
- False
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Recall the definition of Carmichael numbers.
Question 5.
Given a prime p = 17, find an integer a that satisfies Fermat's Little Theorem, and prove it.
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Reduce 10^(16) step by step modulo 17.
Question 6.
For the Carmichael number 561, show all bases up to 10 satisfy Fermat's Little Theorem.
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Recall the properties of modular arithmetic.

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