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Department:

MATH

Course Number:

4150

Hours - Lecture:

3

Hours - Lab:

0

Hours - Recitation:

0

Hours - Total Credit:

3

Typical Scheduling:

Every spring semester

Primes and unique factorization, congruences, Chinese remainder theorem, Diophantine equations, Diophantine approximations, quadratic reciprocity. Applications such as fast multiplication, factorization and encryption.

Course Text:

At the level of *Elementary Number Theory and Its Applications*, Kenneth H. Rosen, 5th ed. Pearson/Addison Wesley

Topic Outline:

- 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