  We investigate the robustness of Majorana edge modes under disorder and
interactions. We exploit a recently found mapping of the interacting Kitaev
chain in the symmetric region ($\mu = 0$, $t = \Delta$) to free fermions.
Extending the exact solution to the disordered case allows us to calculate
analytically the topological phase boundary for all interaction and disorder
strengths, which has been thought to be only accessible numerically. We
discover a regime in which moderate disorder in the interaction matrix elements
enhances topological order well into the strongly interacting regime $U > t$.
We also derive the explicit form of the many-body Majorana edge wave function
revealing how it is dressed by many-particle fluctuations from interactions.
The qualitative features of our analytical results are valid beyond the
fine-tuned integrable point as expected from the robustness of topological
order and as corroborated here by an exact diagonalization study of small
systems.
