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I took a very basic intro to number theory course last semester. We learned about many of the standard topics (gcd, primes, cryptography, congrences, pythagorean triples, etc), but we never learned anything about quadratic reciprocity. I've been skimming over the wikipedia article on it and want to learn more.

What are the best resources (number theory texts, lecture notes, videos, etc) for a gentle introduction to and proof of the quadratic reciprocity theorem?

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I definitely recommend Number Theory by George Andrews. It's a very comprehensive book, short sweet and cheap. his writing style and his ability to look at results from different angles is excellent. It's a very enjoyable book.

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I really like "An Introduction to the Theory of Numbers" by Niven, Zuckerman and Montgomery. Great collection of problems too.

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  • $\begingroup$ Second that, oldie but goodie. One should not forget about a primary author, Ivan Niven. $\endgroup$ – André Nicolas Jul 13 '14 at 3:04
  • $\begingroup$ I knew I was forgetting somebody! Thank you. $\endgroup$ – Memeozuki Jul 13 '14 at 3:46
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I'm enjoying this library book, Introduction to Number Theory by Daniel E. Flath. Pretty similar topics to the type of answers I generally give on MSE. It really is pretty basic, but I do think a semester of abstract algebra (groups, rings, fields) and one of linear algebra/matrix theory would help. I ordered a used copy online for myself, inexpensive.

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