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 A356711 Numbers k such that Mordell's equation y^2 = x^3 + k^3 has exactly 5 integral solutions. 8
 1, 4, 9, 10, 14, 16, 25, 28, 33, 36, 37, 40, 49, 64, 70, 81, 84, 88, 90, 91, 100, 104, 121, 126, 130, 132, 140, 144, 154, 160, 169, 176, 184, 193, 196 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Cube root of A179149. Contains all squares: suppose that y^2 = x^3 + t^6, then (y/t^3)^2 = (x/t^2)^3 + 1. The elliptic curve Y^2 = X^3 + 1 has rank 0 and the only rational points on it are (-1,0), (0,+-1), and (2,+-3), so y^2 = x^3 + t^6 has 5 solutions (-t^2,0), (0,+-t^3), and (2*t^2,+-3*t^3). LINKS Table of n, a(n) for n=1..35. EXAMPLE 1 is a term since the equation y^2 = x^3 + 1^3 has 5 solutions (-1,0), (0,+-1), and (2,+-3). CROSSREFS Cf. A081119, A179145, A179147, A179149, A179151, A356709, A356710, A356712. Indices of 5 in A356706, of 2 in A356707, and of 3 in A356708. Sequence in context: A208980 A010426 A243170 * A054294 A198097 A358762 Adjacent sequences: A356708 A356709 A356710 * A356712 A356713 A356714 KEYWORD nonn,hard,more AUTHOR Jianing Song, Aug 23 2022 EXTENSIONS a(31)-a(35) from Max Alekseyev, Jun 01 2023 STATUS approved

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Last modified November 29 13:49 EST 2023. Contains 367445 sequences. (Running on oeis4.)