login
Numbers k such that Mordell elliptic curve y^2 = x^3 + k has a number of integral points that is both odd and > 1.
4

%I #28 Sep 24 2022 12:33:01

%S 1,8,64,343,512,729,1000,1331,2744,4096,5832,9261,10648,12167,15625,

%T 17576,21952,32768,35937,39304,42875,46656,50653,54872,64000,85184,

%U 97336,117649,125000,175616,185193,250047,262144,274625,343000,357911,373248,405224,474552,531441,592704,636056

%N Numbers k such that Mordell elliptic curve y^2 = x^3 + k has a number of integral points that is both odd and > 1.

%C Cubes k such that y^2 = x^3 + k has a solution other than (-k^(1/3), 0).

%C Contains all sixth powers since A179149 does.

%H Jianing Song, <a href="/A356703/b356703.txt">Table of n, a(n) for n = 1..85</a>

%F a(n) = A356720(n)^3.

%e 512 is a term since the equation y^2 = x^3 + 512 has 9 integral solutions (-8,0), (-7,+-13), (4,+-24), (8,+-32), and (184,+-2496).

%Y Complement of A179145 among the positive cubes.

%Y Cf. A081119, A179147, A179149, A179151, A179163, A179419.

%Y Cf. also A356709, A356720, A356713, A228948.

%K nonn

%O 1,2

%A _Jianing Song_, Aug 23 2022