Rigor in number theory
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.
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.
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 . 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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