On endomorphisms of free groups that preserve primitivity

It is proven that if phi is an endomorphism of a free group F-n = < x(1),...,x(n)> of rank n such that phi(u) is primitive whenever so is u is an element of F-n and phi(F-n) contains a primitive pair (i.c., a pair alpha(x(1)), alpha(x(2)) with alpha is an element of Aut F-n), then phi is an automorphism. Also, every endomorphism of F-2 that preserves primitivity is an automorphism.