intermediate

Number theory

Comprehensive AI-generated study curriculum with 1 detailed note module.

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Course Syllabus

  1. Foundations of Prime and Composite Numbers
  2. Methods for Generating Prime Numbers
  3. Mersenne Primes
  4. Fermat's Primes (Conceptual Introduction)
  5. The Fundamental Theorem of Arithmetic and Factorization
  6. Applications of Primes in Cryptography
  7. Advanced Properties and Ongoing Research

Study Notes

Foundations of Prime and Composite Numbers

You're probably used to multiplying numbers to get larger ones. Now, let's look at numbers by dividing them. When you divide a whole number by another whole number and get no remainder, the number you divided by is called a factor.

A factor of a number is any whole number that divides into it evenly (with no remainder).
* For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. Why?
* 12 ÷ 1 = 12
* 12 ÷ 2 = 6
* 12 ÷ 3 = 4
* 12 ÷ 4 = 3
* 12 ÷ 6 = 2
* 12 ÷ 12 = 1

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