Numbers of solutions of equations in finite fields

@article{Weil1949NumbersOS,
  title={Numbers of solutions of equations in finite fields},
  author={Andr{\'e} Weil},
  journal={Bulletin of the American Mathematical Society},
  year={1949},
  volume={55},
  pages={497-508}
}
  • A. Weil
  • Published 1 May 1949
  • Mathematics
  • Bulletin of the American Mathematical Society
Such equations have an interesting history. In art. 358 of the Disquisitiones [1, a], Gauss determines the Gaussian sums (the so-called cyclotomic “periods”) of order 3, for a prime of the form p = 3n + 1, and at the same time obtains the number of solutions for all congruences ax− by ≡ 1 (mod p). He draws attention himself to the elegance of his method, as well as to its wide scope; it is only much later, however, viz. in his memoir on biquadratic residues [1, b], that he gave in print another… 

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