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

L. J. Mordell

A chapter in Number Theory and Analysis, 1969, pp 223-232 from Springer

Abstract: Abstract The simplest Diophantine equation of degree greater than 2 is the equation (1) $$ y^2 = x^3 + k $$ 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.

Date: 1969
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DOI: 10.1007/978-1-4615-4819-5_15

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