  Recently two interesting conjectures about the string S-matrix on AdS_5 x S^5
have been made. First, assuming the existence of a Hopf algebra symmetry Janik
derived a functional equation for the dressing factor of the quantum string
Bethe ansatz. Second, Hernandez and Lopez proposed an explicit form of
1/\sqrt\lambda correction to the dressing factor. In this note we show that in
the strong coupling expansion Janik's equation is solved by the dressing factor
up to the order of its validity. This observation provides a strong evidence in
favor of a conjectured Hopf algebra symmetry for strings in AdS_5 x S^5 as well
as the perturbative string S-matrix.
