Math 567 - Elementary Number Theory

• Prerequisites: Math 340 or con reg.
• Frequency: Fall (I)
• Student Body: Math majors and graduate students in related areas
• Credits: 3. (N-A)
• Recent Texts: Elementary Number Theory, David M. Burton
• Course Coordinator: Ken Ono
• Background and Goals: This course is an undergraduate introduction to number theory.
• Alternatives: N/A
• Subsequent Courses: N/A

Content coverage:

• Divisibility, the Euclidean algorithm and the GCD, linear Diophantine equations, prime numbers and uniqueness of factorization.
• Congruences, Chinese remainder theorem, Fermat's "little" theorem, Wilson's theorem, Euler's theorem and totient function, the RSA cryptosystem.
• Number-theoretic functions, multiplicative functions, Mobius inversion.
• Primitive roots and indices.
• Quadratic reciprocity and the Legendre symbol.
• Perfect numbers, Mersenne primes, Fermat primes.
• Pythagorean triples, Fermat's "last" theorem with proofs of special cases.
• Fibonacci numbers.
• Continued fractions.
• Distribution of primes, discussion of prime number theorem.
• Primality testing and factoring algorithms.