Primes and unique factorization, congruences, Chinese remainder theorem, Diophantine equations, Diophantine approximations, quadratic reciprocity. Applications such as fast multiplication, factorization and encryption.
At the level of Elementary Number Theory and Its Applications, Kenneth H. Rosen, 5th ed. Pearson/Addison Wesley
- Prime numbers; sieve of Eratosthenes; unique factorization; congruence modulo n; Euclidean algorithm; Chinese Remainder Theorem
- Arithmetic functions (\phi, \sigma, \mu, d); Fermat's (little Theorem); primitive roots; quadratic residues; reciprocity
- Some elementary Diophantine equations (Pythagorean triples, sums of squares)
- Primality testing; factorization; applications to cryptography