Practice Applications Of Fermat's Little Theorem (12.1.5) - Introduction to Fermat’s Little Theorem and Primality Testing

Practice: Applications of Fermat's Little Theorem

Lesson 12.1.5Introduction to Fermat’s Little Theorem and Primality Testing

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8 questions

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6 sample questions

Question 1.
What does Fermat's Little Theorem state?
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Focus on the conditions involving **p** and **a**.
Question 2.
Give an example of a number that is co-prime to 7.
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Think about multiples.
3Question 3.
What does Fermat's Little Theorem allow us to conclude if b^(p-1) ≡ 1 (mod p)?
- **p is prime**
- **p is composite**
- **a is prime**
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Remember valid conditions of the theorem.
4Question 4.
Is the statement 'All Carmichael numbers are prime' true?
- True
- False
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Recall the definition of a Carmichael number.
Question 5.
Using Fermat's Little Theorem, prove that a^(p-1) ≡ 1 (mod p) holds for large p and any a co-prime to it. Provide an example.
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Select a prime larger than 10.
Question 6.
Explore the implications of Carmichael numbers. Investigate if any Carmichael numbers exist and discuss their significance.
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Use online mathematical databases or number theory resources.

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