MATH 509 Elementary Number Theory

Prerequisites: MATH 505, and enrollment in the High School Track of the MS in Mathematics Education program or an undergraduate degree in mathematics, or permission of the instructor. An introduction to the theory of numbers: divisibility, prime numbers, unique factorization, congruences, Euler's phi-function, Fermat's and Wilson's theorems, multiplicative functions, quadratic reciprocity, perfect numbers, and applications to Diophantine equations. Applications include public-key cryptography and integer arithmetic.