id:A081120 - OEIS Search Results

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Number of integral solutions to Mordell's equation y^2 = x^3 - n.

+0
7

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; listen)

	OFFSET	`1,2`
	COMMENT	`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.`
	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.`
	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`
	CROSSREFS	`Cf. A081119, A081121.` `Sequence in context: A099894 A048298 A123565 this_sequence A102392 A051517 A053118` `Adjacent sequences: A081117 A081118 A081119 this_sequence A081121 A081122 A081123`
	KEYWORD	`nice,nonn`
	AUTHOR	`T. D. Noe (noe(AT)sspectra.com), Mar 06 2003`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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