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%I #12 Apr 01 2018 12:55:00
%S 1,1,1,4,4,-5
%N Integer solutions x, y, z of x^3 + y^3 + z^3 = 3 with |x| <= |y| <= |z|.
%C It is conjectured that no other solution exists.
%C Cassels proved that x == y == z (mod 9), noting first that x == y == z == 1 (mod 3) and then using the law of cubic reciprocity.
%H J. W. S. Cassels, <a href="http://www.ams.org/journals/mcom/1985-44-169/S0025-5718-1985-0771049-4/S0025-5718-1985-0771049-4.pdf">A note on the diophantine equation x^3 + y^3 + z^3 = 3</a>, Math. Comp., 44 (1985), 265-266.
%e 1^3 + 1^3 + 1^3 = 3 = 4^3 + 4^3 + (-5)^3.
%K sign,hard,more
%O 1,4
%A _Jonathan Sondow_, Apr 01 2014