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    How do you develop the theory of integers from first principles, up to quadratic reciprocity?

    Is there a common set of axioms?

    I mean number theory, ignoring the real and rational numbers and theorems resulting from them, just the theory of integers.
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    (Original post by nolifer)
    How do you develop the theory of integers from first principles, up to quadratic reciprocity?
    A fairly standard way to start is given here and here. These constructions get you as far as \mathbb{Z}. Once you have got this far, you can proceed to things like quadratic reciprocity in the usual way that number theory texts do it!
 
 
 
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Updated: March 23, 2016

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