%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