Experimental Number Theory (Oxford Graduate Texts in Mathematics)

the long version

"This graduate text is intended for first or second year graduate students in pure mathematics. The main goal of the text is to show how the computer can be used as a tool for research in Number Theory through numerical experimentation. The book contains many examples of experiments in elementary class field theory, binary quadratic forms, sequences, combinatories, p-adic numbers and polynomials, along with exercises and selected remarks and solutions. The numerous routines used in the examples are written in GP, the scripting language of the computational package PARI, and are available for download from the author's website."--Jacket.