  We generalize Greenberger-Horne-Zeilinger (GHZ) theorem to an arbitrary
number of D-dimensional systems. Contrary to conventional approaches using
compatible composite observables, we employ incompatible and concurrent
observables, whose common eigenstate is still a generalized GHZ state. It is
these concurrent observables which enable to prove a genuinely N-partite and
D-dimensional GHZ theorem. Our principal idea is illustrated for a four-partite
system with D which is an arbitrary multiple of 3. By extending to N qudits, we
show that GHZ theorem holds as long as N is not divisible by all nonunit
divisors of D, smaller than N.
