Ebook: Lectures on Elementary Number Theory

Using a background of analysis and algebra, the reader is led to the fundamental theorems of number theory; the uniqueness of prime number factorization and the reciprocity law of quadratic residues. Cyclotomy is treated in some detail because of its own significance and as a framework for the elegant theorems on Gaussian sums. Asymptotic laws are discussed as a foretaste of analytic number theory; also, Dirichlet's theorem about primes in an arithmetic progression and V. Brun's theorem on twin primes.