OFFSET
1,3
COMMENTS
Terms are arranged in order of increasing absolute value (if equal, the negative number comes first).
LINKS
Beniamino Segre, On the rational solutions of homogeneous cubic equations in four variables, Math. Notae, 11 (1951), 1-68.
EXAMPLE
2*25^3 + 2*(-64)^3 + 79^3 = 2*164^3 + 2*(-167)^3 + 79^3 = 1, 79 is a term.
MATHEMATICA
Clear[t]
t = {};
Do[y = ((1 - 2x^3 - z^3)/2)^(1/3) /. (-1)^(1/3) -> -1;
If[IntegerQ[y] && GCD[x, y, z] == 1, AppendTo[t, z]], {z, -4000, 4000}, {x, -Round[(Abs[1 + z^3]/6)^(1/2)], Round[(Abs[1 + z^3]/6)^(1/2)]}]
u = Union@t;
v = Table[(-1)^n*Floor[(n + 1)/2], {n, 0, 8001}];
Select[v, MemberQ[u, #] &]
CROSSREFS
KEYWORD
sign
AUTHOR
XU Pingya, Oct 18 2020
STATUS
approved