University Mathematics
Number Theory
Divisibility, primes and congruences: elementary number theory with its classical theorems and its modern use in cryptography.
Curriculum / Syllabus
- Divisibility, the Division Algorithm and the Euclidean Algorithm
- Primes and the Fundamental Theorem of Arithmetic
- Congruences and Linear Congruences
- The Chinese Remainder Theorem
- Fermat's Little Theorem and Euler's Theorem
- Arithmetic Functions
- Primitive Roots, Quadratic Residues and RSA
Exam & Course Strategy
Exams combine short proofs with computations such as solving congruences and finding modular inverses. Fluency with the Euclidean algorithm and modular arithmetic saves a great deal of time.