On Some Diophantine Equations y2 = x3 + k with no Rational Solutions (II)

  • L. J. Mordell


The simplest Diophantine equation of degree greater than 2 is the equation
$$ y^2 = x^3 + k $$
where k is an integer. Two problems arise according as rational solutions or integral solutions are required. It is the problem of rational solutions which will be discussed here. No finite algorithm is known for finding solutions if they exist, except for special values of k.


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Copyright information

© Springer Science+Business Media New York 1969

Authors and Affiliations

  • L. J. Mordell
    • 1
  1. 1.CambridgeUK

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