Abstract
Using Eisenstein's law of cubic reciprocity we investigate cases in whichx 3=y 2+k is unsolvable in the ring of rational integers ℂ In particular we show, that for all primesp ≢ ± 1 (mod 9),p≠3, the equationx 3=y 2+3p(p±9) has no solutions in ℂ.
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Felgner, U. On Bachet's diophantine equationx 3=y 2=k . Monatshefte für Mathematik 98, 185–191 (1984). https://doi.org/10.1007/BF01507747
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DOI: https://doi.org/10.1007/BF01507747