Here's the question: The Lucas numbers Ln are defined by the equations L1=1 and Ln=Fn+1 + Fn-1 for each n>/= 2. Fn stands for a fibonacci number, Fn= Fn=1 + Fn-2. Prove that Ln=Ln-1+Ln-2 (for n>/= 3) So I did the base case where n=3, but I am stuck on the induction step... Any ideas? Then the problem asks "what is wrong with the following argument?" "Assuming Ln=Fn for n=1,2,...,k we see that Lk+1=Lk=Lk-1 (by the above proof) =Fk+Fk-1 (by our assumption) =Fk+1 (by definition of Fk+1) Hence by the principle of mathematical induction Fn=Ln for each positive n." Any help would be greatly appreciated!