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%I #17 Aug 06 2022 03:02:46
%S 6,9,12,16,19,20,25,27,28,29,34,39,40,41,44,46,51,53,54,55,58,60,67,
%T 69,70,71,72,75,76,80,81,82,84,85,87,88,89,90,93,94,96,97,98,99,102,
%U 103,105,108,109,110,111,113,115,116,120,121,122,123,126,127,129,132,134,137,139
%N w such that w^3+x^3+y^3+z^3=0, w>|x|>|y|>|z|, is soluble.
%D J. Leech, Some solutions of Diophantine equations, Proc. Camb. Phil. Soc., 53 (1957), 778-780, see p. 799.
%D H. W. Richmond, On integers which satisfy ..., Trans. Camb. Phil. Soc., 22 (1920), 389-403, see p. 402.
%t sol[w_] := Reap[ Do[ If[ GCD[w, x, y, z] == 1 && w > Abs[x] > Abs[y] > Abs[z] && w^3 + x^3 + y^3 + z^3 == 0, Print[{w, x, y, z}]; Sow[{w, x, y, z}]; Break[]], {x, -w+1, -1}, {y, x+1, -1}, {z, y+1, -y-1}]][[2]]; Select[ Range[140], sol[#] =!= {} & ] (* _Jean-François Alcover_, Feb 24 2012 *)
%Y Cf. A001235.
%K nonn,nice
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _David W. Wilson_
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