Abstract :
LetFmbe a free group of finite rankm. It is proven that for everyn ≥ 2 there is a non-trivial wordwn(x1,…,xn) such that if valueswn(Un), wn(Vn) ofwn(x1,…,xn) on twon-tuplesUnandVnof elements ofFmare conjugate and non-trivial then thesen-tuples themselves are conjugate. As a corollary, one has the existence of two elements inFmwhose images uniquely determine any monomorphism ψ:Fm → Fm.
