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

Scarowsky, Manny

doi:10.1090/S0002-9939-1984-0744627-7

On units of certain cubic fields and the Diophantine equation $x^{3}+y^{3}+z^{3}=3$
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Proc. Amer. Math. Soc. 91 (1984), 351-356 Request permission

Abstract:

The Diophantine equation ${x^3} + {y^3} + {z^3} = 3$ 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.

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