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Does anyone know any simple/nice applications of class field theory? I would really like to find one related to diophantine equations, but anything you got would be good.

Thanks

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    I am told that Cox's _Primes of the form $x^2 + ny^2$_ is a good resource for this. Class field theory can help answer the question of, well, which primes can be represented in the form $x^2 + ny^2$ for fixed $n$.2012-03-14
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    Cox's book is great, I was wondering if there was any other examples, like x2+ny2, where class field theory helps.2012-03-14

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