  We give the basic definitions and some theoretical results about
hyperdeterminants, introduced by A. Cayley in 1845. We prove integrability
(understood as 4d-consistency) of a nonlinear difference equation defined by
the 2x2x2-hyperdeterminant. This result gives rise to the following hypothesis:
the difference equations defined by hyperdeterminants of any size are
integrable.
  We show that this hypothesis already fails in the case of the
2x2x2x2-hyperdeterminant.
