
Understanding Fermat's Little Theorem and Prime Testing

Interactive Video
•
Mathematics, Science
•
9th - 12th Grade
•
Hard

Emma Peterson
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does Fermat's Little Theorem state about prime numbers?
A number raised to a prime power minus the number itself is divisible by the prime.
A number is prime if it passes the Baillie-PSW test.
A number is prime if it is only divisible by 1 and itself.
A number is composite if it can be divided by any number other than 1 and itself.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example using the number 5, which of the following calculations is NOT divisible by 5?
2⁵ - 2
1⁵ - 1
4⁵ - 4
3⁵ - 3
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a Fermat liar?
A number that is actually prime but fails Fermat's test.
A composite number that passes Fermat's test for a specific base.
A prime number that passes Fermat's test for all bases.
A composite number that fails Fermat's test for all bases.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a Fermat witness?
A number that fails Fermat's test for all bases.
A number that passes Fermat's test for all bases.
A number that shows a composite number is not prime.
A number that proves a composite number is actually prime.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is unique about Carmichael numbers?
They are prime numbers that fail Fermat's test.
They are composite numbers that pass Fermat's test for all bases.
They are numbers that pass the Baillie-PSW test.
They are numbers that are divisible by 1 and themselves only.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following is the first Carmichael number?
341
25
1729
561
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main limitation of Fermat's test as discussed in the video?
It requires complex calculations.
It can incorrectly identify composite numbers as prime.
It is too slow for large numbers.
It cannot identify any prime numbers.
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