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A081120
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Number of integral solutions to Mordell's equation y^2 = x^3 - n.
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19
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1, 2, 0, 4, 0, 0, 4, 1, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 4, 1, 6, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 0, 2, 2, 0, 6, 4, 2, 0, 0, 0, 4, 2, 4, 2, 0, 0, 0, 4, 2, 0, 4, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 4, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 6
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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. See A081119 for the number of integral solutions to y^2 = x^3 + n.
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REFERENCES
| 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
| T. D. Noe, Table of n, a(n) for n=1..10000 (from Gebel)
J. Gebel, Integer points on Mordell curves
Eric Weisstein's World of Mathematics, Mordell Curve
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CROSSREFS
| Cf. A081119, A081121.
Sequence in context: A099894 A048298 A123565 * A200038 A102392 A051517
Adjacent sequences: A081117 A081118 A081119 * A081121 A081122 A081123
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KEYWORD
| nice,nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Mar 06 2003
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