13.66 (1995)

Let $F$ be a
$\qquad$ a) free;
$\qquad$ b) free metabelian
group of finite rank. Let $M$ denote the set of all endomorphisms of $F$ with non-cyclic images. Can one choose two elements $g, h \in F$ such that, for every $\varphi, \psi \in M$, equalities $\varphi(g) = \psi(g)$ and $\varphi(h) = \psi(h)$ imply that $\varphi = \psi$, that is, the endomorphisms in $M$ are uniquely determined by their values at $g$ and $h$?