# 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} }

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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