References E.2 General References
There are many good introductory number theory texts.
A good introduction with an emphasis on groups, containing interleaved exercises with full answers.
A highly regarded text with copious notes, but sometimes more than a little hard to parse with its consecutively numbered theorems and very dense prose.
Freely available and the first Sage-enabled number theory text, by the founder of Sage (a number theorist).
A venerable text with programming exercises that still wear well.
The topics are very standard, but the approach is quite different; no proofs, only statements. This turns out to be a highly effective pedagogy; see the Academy of Inquiry Based Learning for more information.
A very fun inquiry-driven text before there were such things, with a lot of extremely good examples, especially in things like quadratic forms.
More algebraically oriented, with good material on the Pell equation and Gaussian integers – noteworthy for a good treatment of Conway's river concepts.
Surprisingly detailed and high-level but has good coverage of several unusual topics such as geometry of numbers.
Yet another nice reprint from Dover, this one with (as one would expect of the author) great combinatorial content.
Not so algorithmic, but very, very concrete and constructive. Squares are \(\square\)s, which grows on the reader.
An out-of-print standard text with many similar topics and interesting historical comments.
An older text that is still worth the conversational tone.
Careful emphasis throughout on getting a novice student ready for abstract algebra/algebraic number theory, with \(\mathbb{Q}[\sqrt{d}]\) coherent in an elementary text. Don't miss continued fractions in the service of the Bezout identity and the many interesting projects, including one on the \(p\)-adic numbers.