Rational Points on Some Fermat Curves and Surfaces over Finite Fields
نویسندگان
چکیده
We give an explicit description of the Fqi-rational points on the Fermat curve uq−1+vq−1+wq−1 = 0, for i ∈ {1, 2, 3}. As a consequence, we observe that for any such point (u, v, w), the product uvw is a cube in Fqi . We also describe the Fq2-rational points on the Fermat surface uq−1 + vq−1 + wq−1 + xq−1 = 0.
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