Algebraic Points of Degree at Most 5 on the Affine Curve y\(^{2}\) = x\(^{5}\) - 243
EL Hadji Sow *
Mathematics and Applications Laboratory (L.M.A.), U.F.R. of Science and Technology, Assane SECK University of Ziguinchor, Senegal.
Pape Modou Sarr
Mathematics and Applications Laboratory (L.M.A.), U.F.R. of Science and Technology, Assane SECK University of Ziguinchor, Senegal.
Oumar Sall
Mathematics and Applications Laboratory (L.M.A.), U.F.R. of Science and Technology, Assane SECK University of Ziguinchor, Senegal.
*Author to whom correspondence should be addressed.
Abstract
In this work, we determine the set of algebraic points of degree at most 5 on the ane curve y2 = x5 - 243. This result extends a result of J.TH Mulholland who described in [4] the set of \(\mathbb{Q}\)- rational points i.e the set of points of degree one over \(\mathbb{Q}\) on this curve.
Keywords: Planes curves, degree of algebraic points, rationals points, algebraic extensions, linear system, jacobian