The background of Kummer's proof of Fermat's last theorem for regular primes

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This article contains a brief review of the circumstances which surrounded Kummer's proof of Fermat's Last Theorem for “regular” prime exponents. The often-told story that this proof developed out of an earlier proof which was fallacious is questioned, and a new document, an unknown letter from Liouville to Dirichlet which is related to this history, is presented. Also presented is the little-known fact that Kummer's theory of “ideal complex numbers”, which was the basis of the proof, contained a serious flaw which went uncorrected for ten years.

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Communicated by M. Kline

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Edwards, H.M. The background of Kummer's proof of Fermat's last theorem for regular primes. Arch. Rational Mech. 14, 219–236 (1975). https://doi.org/10.1007/BF00327448

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Keywords

  • Complex Number
  • Fermat
  • Ideal Complex
  • Early Proof
  • Prime Exponent