We show that the affine surfacesx3+y3+cz3=c, c ∈Q, in the casesc≠2,c=2, contain precisely 2, respectively 4, polynomial parametric solutions corresponding to curves of arithmetic genus 0 on the surface.
However, these surfaces contain infinitely many polynomial parametric solutions corresponding to curves of arithmetic genus greater than 0.
KeywordsNumber Theory Algebraic Geometry Topological Group Parametric Solution Arithmetic Genus
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