Math majors and graduate students in related areas
This course is an undergraduate introduction to number theory.
- 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.