Number Theory: In Context and Interactive

Oodles of class-tested historical material and many, many exercises, including a welter of them on topics surrounding amicable numbers.

A very nice historically-oriented approach to elementary number theory. Includes Sage material in an appendix.

Another conversational classic by Ore, with plenty of historical goodies.

A truly historical sojourn through much of number theory up through the early twentieth century, with extensive primary source material and investigation of Gauss’ monumental work. Sadly, largely beyond the level of this text.

This is intended for those without calculus, but has many great number-theoretic bits all the same.

This book has some nice discussion of Euler’s number theory alongside many other historical vignettes with real math power.

Collection of additional classroom resources focused on primary source material, including the Basel problem and quadratic reciprocity.

Absolutely first-rate mathematician’s insider view into the contributions of Fermat and Euler. Plenty of opinions and connections to modern mathematics, though sadly it will never be updated to connect Wiles’ work on elliptic curves to Fermat’s legacy.

In general it’s accessible to a student using this book, though as a reprint of a fifty-year-old book it (as a recent College Mathematics Journal review put it) could use ‘certain updates’.

Reprint of MIT Press original publication (now out of print), an extremely thorough discussion of Qin Jiushao’s entire mathematical opus within its cultural context. About half the book is a monograph on the Chinese Remainder Theorem, hence its inclusion in this set of references.

Special focus on number theory in the medieval era in the Islamic world, especially Persian mathematicians. Many explicit examples, and comparisons with Diophantus and more modern sources.

More information than you would ever want to know about Apéry’s constant, by an engaging author. Many computations.