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March 31st, 2014, 04:39 AM   #11
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Originally Posted by mathbalarka View Post
@Gregory : Do you know modular arithmetic and p-adics?
I have a rudimentary understanding of modular arithmetic. I'm not at all familiar with the workings of the p-adic number system.
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March 31st, 2014, 05:06 AM   #12
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You should try Niven-Zuckerman-Montgomery. Lots of exercises to work out.
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April 28th, 2015, 12:12 PM   #13
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Ireland & Rosen's NT intro is a perfect example of how editors mislead the public to sell books, there is nothing like "intro" in that book. The same goes for a bunch of "intro's", take Van Dalen's intro do logic, at least Ireland & Rosen is well done, clear and with many references, although the experience in algebra it demands obviously is not possessed by anyone who is not already quite familiar with number theory.

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Ireland & Rosen is what I learned number theory from, but I don't recommend it for beginners. It's better for a second course in (algebraic) number theory. Similarly, I find Apostol too advanced. In a pinch you could start with Hardy & Wright but you won't get far if you lack other experience.

The other suggestions are probably more appropriate.
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April 28th, 2015, 12:53 PM   #14
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Ireland & Rosen's NT intro is a perfect example of how editors mislead the public to sell books, there is nothing like "intro" in that book.
It's an introduction to modern number theory, not a modern introduction to number theory. The title is apt.
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April 28th, 2015, 01:37 PM   #15
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Oh, all clear then, sure no one would think that this is not intended as a first course in number theory given the positioning of the adjective.

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Originally Posted by CRGreathouse View Post
It's an introduction to modern number theory, not a modern introduction to number theory. The title is apt.
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April 29th, 2015, 01:36 AM   #16
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There is a very nice introduction to NT with answers to all exercises, and especial chapters on FLT and the Zeta Function:

Elementary Number Theory (Springer Undergraduate Mathematics Series): Gareth A. Jones, Josephine M. Jones: 9783540761976: Amazon.com: Books

Since it has answers to ALL exercises I think it is a good book to consult, it is very problem-solving oriented, so you get many techniques with work examples.

Then, before Ireland&Rosen sort of book, another very didactic book on ALgebra is:

http://www.amazon.com/Book-Abstract-.../dp/0486474178

This is the best possible value for the money.



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I have a rudimentary understanding of modular arithmetic. I'm not at all familiar with the workings of the p-adic number system.
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