• DOI:10.1007/978-1-4612-1974-3_18
Corpus ID: 118434795

Class Field Theory and the First Case of Fermat’s Last Theorem

@inproceedings{Lenstra1997ClassFT,
  title={Class Field Theory and the First Case of Fermat’s Last Theorem},
  author={H. Lenstra and P. Stevenhagen},
  year={1997}
}

H. Lenstra, P. Stevenhagen

Published 1997

Mathematics

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For a prime number p, the first case of Fermat’s last theorem for exponent p asserts that for any three integers x, y, z with xp+yp+zp=O at least one of x, y, z is divisible by p. In the present chapter we use class field theory to prove several classical results concerning the first case. Our treatment is based on Hasse’s exposition [6, Section 22], but whereas Hasse applied explicit reciprocity laws, our proofs depend only on general properties of power and norm residue symbols.