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$K=Q(\zeta_n)$ a cyclotomic extension: $p$ splits completely in $K$ if and only if $p\equiv 1\ (mod\ n)$

I don't know how i could prove, I search a kind of cyclotomic reciprocity law

Many thanks

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    Might I refer you to the book: *Algebraic Number Theory* by **Jürgen Neukirch**? It is a complete and reasonably arranged book. (http://www.amazon.com/Algebraic-Number-Grundlehren-mathematischen-Wissenschaften/dp/3540653996)2012-02-07

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