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Is there a good textbook that will help me understand the motivation for defining the Legendre symbol (and it's Jacobi generalization), and applications of them to number theory? I have a math degree and I am comfortable with graduate-level texts.

Thank you.

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    $\begingroup$ Apostol's book is the reference, even if the proofs can be hard to follow $\endgroup$
    – reuns
    Aug 2, 2017 at 20:18

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One of the best books I know for these topics is A Classical Introduction to Modern Number Theory by Ireland and Rosen. In particular, see Chapter $5$ on quadratic reciprocity, and for its generalisations in Chapter 9, on cubic and biquadratic reciprocity.

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