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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A356711 Numbers k such that Mordell's equation y^2 = x^3 + k^3 has exactly 5 integral solutions.

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%I A356711 #16 Jun 06 2023 17:40:44
%S A356711 1,4,9,10,14,16,25,28,33,36,37,40,49,64,70,81,84,88,90,91,100,104,121,
%T A356711 126,130,132,140,144,154,160,169,176,184,193,196
%N A356711 Numbers k such that Mordell's equation y^2 = x^3 + k^3 has exactly 5 integral solutions.
%C A356711 Cube root of A179149.
%C A356711 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).
%e A356711 1 is a term since the equation y^2 = x^3 + 1^3 has 5 solutions (-1,0), (0,+-1), and (2,+-3).
%Y A356711 Cf. A081119, A179145, A179147, A179149, A179151, A356709, A356710, A356712.
%Y A356711 Indices of 5 in A356706, of 2 in A356707, and of 3 in A356708.
%K A356711 nonn,hard,more
%O A356711 1,2
%A A356711 _Jianing Song_, Aug 23 2022
%E A356711 a(31)-a(35) from _Max Alekseyev_, Jun 01 2023