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The Diophantine equation      x 3 + y 3 + z 3 = 3 {x^3} + {y^3} + {z^3} = 3       is replaced by a sequence of parametrized Diophantine equations which can be factored in certain cubic fields. A unit in these fields is readily available. Some results about these fields and the parametrized equations are proved.

On units of certain cubic fields and the Diophantine equation 𝑥³+𝑦³+𝑧³=3