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Université de Fribourg

Permutation invariant properties of primitive cubic quadruples

Hürlimann, Werner

In: The Ramanujan Journal, 2017, vol. 43, no. 3, p. 649–662

Based on a specific quadratic Hopf map between the Euclidean spaces of dimension four and three that is associated with Euler’s complete rational parameterization of the four cubes equation, we study the permutation invariant properties of the primitive integer cubic quadruples that solve this equation. Fixing the coordinate with maximum height and taking it positive, our main result...