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 2012-12-31, 06:22 #1 jinydu     Dec 2003 Hopefully Near M48 2×3×293 Posts Factorization of Ideals in Number Field, Looking for Reference Let K be the number field $\mathbb{Q}(2^{1/3})$. Find the factorizations of (7), (29) and (31) in $O_K$. I know there's a theorem by Kronecker that says (7) is reducible iff $x^3\equiv 2 \text{mod }7$, has a solution (or something like that) and how to find the factorization in the case it does have a solution. But I can't seem to find a reference for this. Can anyone suggest a reference? No spoilers to this problem please, just a reference. Thanks