OFFSET
1,4
COMMENTS
It is conjectured that no other solution exists.
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.
LINKS
J. W. S. Cassels, A note on the diophantine equation x^3 + y^3 + z^3 = 3, Math. Comp., 44 (1985), 265-266.
EXAMPLE
1^3 + 1^3 + 1^3 = 3 = 4^3 + 4^3 + (-5)^3.
CROSSREFS
KEYWORD
sign,hard,more
AUTHOR
Jonathan Sondow, Apr 01 2014
STATUS
approved