MTL145: Number Theory

3 Credits (3-0-0)

Divisibility: basic definition, properties, prime numbers, some results on distribution of primes; Congruences: basic definitions and properties, complete and reduced residue systems, theorems of Fermat, Euler & Wilson, application to RSA cryptosystem, linear congruences and Chinese Remainder theorem, quadratic congruences, and Quadratic Reciprocity law; Arithmetical functions: examples, with some properties and their rate of growth; Continued fractions, and their connections with Diophantine approximatins, applications tolinear and Pell’s equations; Binary quadratic forms; Partition: basic properties and results; Diophatine equations: linear and quadratic, some general equations.