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Algebraic Points of Degree at Most 5 on the Affine Curve y\(^{2}\) = x\(^{5}\) - 243

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.