

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
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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, SpringerVerlag, page 191.
J. Gebel, A. Petho and H. G. Zimmer, On Mordell's equation, Compositio Mathematica 110 (3) (1998), 335367.


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, {}] (* JeanFrançois Alcover, Apr 29 2011 *)


CROSSREFS

Cf. A054504, A081120.
Sequence in context: A128291 A187574 A187833 * A187837 A227455 A237417
Adjacent sequences: A081118 A081119 A081120 * A081122 A081123 A081124


KEYWORD

nice,nonn


AUTHOR

T. D. Noe, Mar 06 2003


STATUS

approved



