# 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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