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Are there any other books which are similarly to the book "Primes of the form $x^2+ny^2$"? Basically, I want a book which starts with a very important classical problem ( in this case which primes can be represented in the form $x^2+ny^2$) ad use that problem as a motivation to introduce one mathematical topic (in this case class field theory and complex multiplication).

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Does it need to follow through with the problem statement throughout the book like Cox does? There are many books that give great, simple problems as motivation to study the subject, but don't follow through as much. For example, I believe it is Koblitz who motivates the study of modular forms by the consideration of the congruent triangle problem. –  Alex Youcis Apr 9 '13 at 14:51
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This thread may be of use. –  Alexander Gruber Apr 9 '13 at 14:56
    
The question @Alex poses is a relevant one. I know quite some books that start out with an interesting problem as motivation, but none that follow the problem throughout. A nice example would be Washington's book on Elliptic Curves, which starts out with a problem about stacking (cannon-)balls. –  HSN Apr 9 '13 at 14:58
    
@AlexYoucis That is not necessary. But it is preferable if it gives some sort of historical (or any other ) motivation for each topic described in the book. –  Mohan Apr 9 '13 at 15:00
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Siegel's first book in his "Topics in Complex Function Theory" series begins with the problem of trying to find an addition formula for certain integrals that aren't expressible in terms of elementary functions, and how that developed into the study of of the Weierstrass $\wp$ function (and more generally elliptic functions). It also develops the beginnings of the theory of Riemann surfaces. Be aware though: the book is definitely not written from a modern perspective. –  Stahl Apr 9 '13 at 15:04

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