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A081121
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Numbers n such that Mordell's equation y^2 = x^3 - n has no integral solutions.
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26
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3, 5, 6, 9, 10, 12, 14, 16, 17, 21, 22, 24, 29, 30, 31, 32, 33, 34, 36, 37, 38, 41, 42, 43, 46, 50, 51, 52, 57, 58, 59, 62, 65, 66, 68, 69, 70, 73, 75, 77, 78, 80, 82, 84, 85, 86, 88, 90, 91, 92, 93, 94, 96, 97, 98, 99
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OFFSET
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1,1
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COMMENTS
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Mordell's equation has a finite number of integral solutions for all nonzero n. Gebel computes the solutions for n < 10^5. Sequence A054504 gives n for which there are no integral solutions to y^2 = x^3 + n. See A081120 for the number of integral solutions to y^2 = x^3 - n.
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REFERENCES
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T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, page 191.
J. Gebel, A. Petho and H. G. Zimmer, On Mordell's equation, Compositio Mathematica 110 (3) (1998), 335-367.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..7759 (from Gebel)
J. Gebel, Integer points on Mordell curves
Eric Weisstein's World of Mathematics, Mordell Curve
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MATHEMATICA
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m = 99; f[_List] := (xm = 2 xm; ym = Ceiling[xm^(3/2)];
Complement[Range[m], Outer[Plus, -Range[0, ym]^2, Range[-xm, xm]^3] //Flatten //Union]); xm=10; FixedPoint[f, {}] (* From Jean-François Alcover, Apr 29 2011 *)
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CROSSREFS
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Cf. A054504, A081120.
Sequence in context: A128291 A187574 A187833 * A187837 A165740 A080307
Adjacent sequences: A081118 A081119 A081120 * A081122 A081123 A081124
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KEYWORD
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nice,nonn
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AUTHOR
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T. D. Noe, Mar 06 2003
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STATUS
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approved
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