A239351 Integer solutions x, y, z of x^3 + y^3 + z^3 = 3 with |x| <= |y| <= |z|.

1, 1, 1, 4, 4, -5

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

Table of n, a(n) for n=1..6.

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

Sequence in context: A372020 A182065 A325487 * A111481 A111763 A159892

Adjacent sequences: A239348 A239349 A239350 * A239352 A239353 A239354

Keyword

sign,hard,more

Author

Jonathan Sondow, Apr 01 2014

Status

approved