Lectures on Elementary Number Theory
Hans Rademacher
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.