The sequence an of non-zero reals satisfies an2 - an-1an+1 = 1 for n ≥ 1. Prove that there exists a real number α such that an+1 = α an - an-1 for n ≥ 1.
For n ≥ 2 define bn = (an + an-2)/an-1. Then the relation given shows that bn+1 = bn.
© John Scholes
12 Dec 1998