Theory of Numbers

Euclid's algorithm and the fundamental theorems on divisibility; prime numbers and congruences; the theorems of Fermat, Euler, and Wilson; quadratic residues and reciprocity law, algebraic numbers, Pythagorian triples, other diophantine equations, Fermat's Last Theorem, Pell's equation and continued fractions, the distribution of prime numbers, and advanced topics.
Note. Three semesters of Calculus are required and must be completed before taking this course.