An ABC construction of number fields

@inproceedings{Roberts2004AnAC,
  title={An ABC construction of number fields},
  author={D. Roberts},
  year={2004}
}
We describe a general three step method for constructing number fields with Lie-type Galois groups and discriminants factoring into powers of specified primes. The first step involves extremal solutions of the matrix equation ABC = I. The second step involves extremal polynomial solutions of the equation A(x) + B(x) + C(x) = 0. The third step involves integer solutions of the generalized Fermat equation axp + byq + czr = 0. We concentrate here on details associated to the third step and give… Expand
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