Practice Examples And Concluding Thoughts (12.5) - Introduction to Fermat’s Little Theorem and Primality Testing

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6 sample questions

Question 1.
What does Fermat's Little Theorem state?
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Look at the conditions involving p and a.
Question 2.
Define a Carmichael number.
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Think of numbers that behave like primes under certain tests.
3Question 3.
What is the significance of Fermat's Little Theorem?
- Proves all numbers are primes
- Forms a basis for primality testing
- Is irrelevant
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Consider its applications in real-life situations.
4Question 4.
True or False: All composite numbers can be identified using Fermat's Little Theorem.
- True
- False
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Think critically about the exceptions in number theory.
Question 5.
Prove that 341 is a false prime using Fermat's theorem.
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Use a base like 2 or 3, and calculate carefully.
Question 6.
Describe an efficient way to test for Carmichael numbers and implement it in a function.
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Look up conditions for known Carmichael numbers.

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