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A054504
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Numbers n such that Mordell's equation y^2 = x^3 + n has no integral solutions.
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32
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6, 7, 11, 13, 14, 20, 21, 23, 29, 32, 34, 39, 42, 45, 46, 47, 51, 53, 58, 59, 60, 61, 62, 66, 67, 69, 70, 74, 75, 77, 78, 83, 84, 85, 86, 87, 88, 90, 93, 95, 96, 102, 103, 104, 109, 110, 111, 114, 115, 116, 118, 123, 124, 130, 133, 135, 137, 139, 140, 146, 147, 149, 153, 155
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Mordell's equation has a finite number of integral solutions for all nonzero n. Gebel computes the solutions for n < 10^5. Sequence A081121 gives n for which there are no integral solutions to y^2 = x^3 - n. See A081119 for the number of integral solutions to y^2 = x^3 + n. - T. D. Noe (noe(AT)sspectra.com), Mar 06 2003
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REFERENCES
| T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, page 192.
J. Gebel, A. Petho and H. G. Zimmer, On Mordell's equation, Compositio Mathematica 110 (3) (1998), 335-367.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..6603 (from Gebel)
J. Gebel, Integer points on Mordell curves
Eric Weisstein's World of Mathematics, Mordell Curve
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MATHEMATICA
| m = 155; 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 28 2011 *)
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CROSSREFS
| Cf. A081119, A081121.
Sequence in context: A164018 A156793 A081715 * A190612 A166496 A035110
Adjacent sequences: A054501 A054502 A054503 * A054505 A054506 A054507
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Apr 08 2000
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EXTENSIONS
| Apostol gives all values of n < 100. Extended by David W. Wilson (davidwwilson(AT)comcast.net) Sep 25, 2000
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