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Old 2014-07-30, 11:24   #6
R.D. Silverman
 
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Nov 2003

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Quote:
Originally Posted by jinydu View Post
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.
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