  We prove an integrality result for the value at s=1 of the adjoint L-function
associated to a cohomological cuspidal automorphic representation on GL(n) over
any number field. We then show that primes (outside an exceptional set)
dividing this special value give rise to congruences between automorphic forms.
We also prove a non-vanishing property at infinity for the relevant
Rankin-Selberg L-functions on GL(n) x GL(n).
