A Note on the Diophantine Equation x 3 + y 3 + z 3 = 3

@article{Cassels1985ANO,
title={A Note on the Diophantine Equation x 3 + y 3 + z 3 = 3},
author={John W. Cassels},
journal={Mathematics of Computation},
year={1985},
volume={44},
pages={265}
}
• J. Cassels
• Published 1985
• Mathematics
• Mathematics of Computation
Any integral solution of the title equation has x =y z (9). The report of Scarowsky and Boyarsky  that an extensive computer search has failed to turn up any further integral solutions of the title equation prompts me to give the proof of a result which I noted many years ago and which might be of use in further work (cf. footnote on p. 505 of ). THEOREM. Any integral solution of (1) X3 + y3 + z3 = 3 has (2) x -y -z (9). Proof. Trivially, (3) x -y --z -1 (3). We work in the ring Z[p] of…
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