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The first example of an N=8 supersymmetric extension of the KdV equation ishere explicitly constructed. It involves 8 bosonic and 8 fermionic fields. Itcorresponds to the unique N=8 solution based on a generalized hamiltoniandynamics with (generalized) Poisson brackets given by the Non-associative N=8Superconformal Algebra. The complete list of inequivalent classes ofparametric-dependent N=3 and N=4 superKdVs obtained from the ``Non-associativeN=8 SCA" is also furnished. Furthermore, a fundamental domain characterizingthe class of inequivalent N=4 superKdVs based on the "minimal N=4 SCA" isgiven.Comment: 14 pages, LaTe

Division algebras and extendedN 2, 4, 8 superKdVs