Review List

Euclidean Algorithm, how to find greatest 
common divisor g = (m,a) and integers x,y such that g=mx+ay. 

Primes, Prime factorization, Primes in arithmetic progression, 
Fermat's little theorem and Euler's generalization, Wilson's Theorem 

Pseudoprimality Test

Euler Phi-Function and its properties

Congruences, 
Chinese remainder theorem, 
Computational Techniques, 
Public-Key Cryptography algorithm. 

Solving congruences, explicitely solve ax=b (mod m)
Quadratic congruences mod primes, integers as sum of squares. 

Congruences mod prime powers, 
Hensel's Lemma and its generalization, 
applying it to find solutions of congruences. 

The order of reduced residues mod m. 
Primitive roots, existence for primes and prime powers, 
nonexistence (e.g. mod 2^k). 

Quadratic residues: Euler's criterion, 
Gauss quadratic residue law, computations

Farey Fractions, approximations of irrational numbers by rationals  
Hurwitz theorem

Simple Continued Fractions, computations, periodic continued fractions, 
convergents and their role for approximations of irrational numbers by rationals.