MTL735: Advanced Number Theory

3 Credits (3-0-0)

Overlaps with: MTL145

Divisibility, prime numbers, Bertrand’s theorem, Congruences, complete & reduced residue systems, theorems of Fermat, Euler, Wilson & Wolstenholme, solutions of general congruences, study of linear and system of linear congruences, Chinese Remainder theorem, study of quadratic congruences, Quadratic, Cubic & Biquadratic Reciprocity laws, binary and ternary quadratic forms, Continued fractions, Diophantine approximations and applications to linear and Pell’s equations, Arithmetical functions, properties, rate of growth, Distribution of primes, Dirichlet’s theorem on primes in arithmetic progression, Prime Number theorem, Diophantine equations, special cases of the Fermat equation, introduction to classic and modern techniques.