We prove, under the strong RSA assumption, that the group
of invertible integers modulo the product of two safe primes
is pseudo-free.
More specifically, no polynomial time algorithm can output
(with non negligible probability) an unsatisfiable system of
equations over
the free abelian group generated by the symbols
*g _{1},...,g_{n}*,
together with a solution modulo the product
of two randomly chosen safe primes when