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A081121 Numbers n such that Mordell's equation y^2 = x^3 - n has no integral solutions. 29
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

This is the complement of A106265. - M. F. Hasler, Oct 05 2013

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..7759 (from Gebel)

J. Gebel, Integer points on Mordell curves

Eric Weisstein's World of Mathematics, Mordell Curve

MATHEMATICA

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, {}] (* Jean-Fran├žois Alcover, Apr 29 2011 *)

CROSSREFS

Cf. A054504, A081120.

Sequence in context: A128291 A187574 A187833 * A187837 A239064 A227455

Adjacent sequences:  A081118 A081119 A081120 * A081122 A081123 A081124

KEYWORD

nice,nonn

AUTHOR

T. D. Noe, Mar 06 2003

STATUS

approved

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Last modified October 24 12:34 EDT 2014. Contains 248516 sequences.