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 [3] 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 [2]). 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… Expand
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