mersenneforum.org - View Single Post - Factorization of Ideals in Number Field, Looking for Reference

R.D. Silverman · 2014-07-30, 11:24

Quote:

Originally Posted by jinydu

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

Henri Cohen's book.