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A005988
x^3 + n*y^3 = 1 is solvable.
(Formerly M1732)
3
2, 7, 9, 17, 19, 20, 26, 28, 37, 43, 63, 65, 91, 124, 126, 182, 215, 217, 254, 342, 344, 422, 511, 513, 614, 635, 651, 728, 730, 813, 999, 1001, 1330, 1332, 1521, 1588, 1657, 1727, 1729, 1801, 1876, 1953, 2196, 2198, 2743, 2745, 3155, 3374, 3376
OFFSET
1,1
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
H. C. Williams and C. R. Zarnke, Computation of the solutions of the Diophantine equation x^3+dy^3=1, Proc. Conf. Numerical Maths., Winnipeg (1971), 671-676.
LINKS
István Gaál, László Remete, Solving binomial Thue equations, arXiv:1810.01819 [math.NT], 2018. See 4.1 Solutions for n = 3 p. 6.
H. C. Williams and C. R. Zarnke, Computation of the solutions of the Diophantine equation x^3+dy^3=1, Proc. Conf. Numerical Maths., Winnipeg (1971), 671-676. (Annotated scanned copy)
H. C. Williams and R. Holte, Computation of the solution of x^3 + D y^3 = 1, Mathematics of Computation, Vol. 31, No. 139. (Jul., 1977), pp. 778-785.
MATHEMATICA
m = 400; s = {}; Do[If[x*y < 0, r = Reduce[ n > 0 && x^3 + n*y^3 == 1, n, Integers]; If[r =!= False, AppendTo[s, n /. ToRules[r]]]], {x, -m, m}, {y, -m, m}]; Union[s] [[1 ;; 38]] (* Jean-François Alcover, Jun 08 2011 *)
CROSSREFS
Sequence in context: A042345 A041973 A042807 * A199537 A079326 A055673
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, Nov 17 2016
STATUS
approved