Fermat's little theorem

High school (ages 12+)
Mathematics & Numbers

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Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/fermats-little-theorem

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the mathematical discipline?Number Theory, specifically elementary number theory
2. What is the discoverer?Pierre de Fermat
3. Why does the theorem only work for prime numbers?Prime numbers have special properties that make the rule true for all of them, but it does not hold for composite numbers.
4. How can Fermat's Little Theorem help find prime numbers?It is used in a quick test called the Fermat primality test. If a number fails the test for some a, the number is definitely not prime.

Modular Arithmetic: A system of arithmetic for integers, where numbers 'wrap around' upon reaching a certain value (the modulus).
Prime Number: A natural number greater than 1 that has no positive divisors other than 1 and itself.
Congruence: A relation indicating that two numbers have the same remainder when divided by a given number (the modulus).
Cryptography: The practice and study of techniques for secure communication in the presence of adversaries.