IMO 1976 LL SWE34

Origin: SWE

Problem

Let {an}\infty and {bn}\infty be two sequences determined by the recursion formulas an+1 = an + bn, bn+1 = 3an + bn, n = 0, 1, 2, . . ., and the initial values a0 = b0 = 1. Prove that there exists a uniquely determined constant c such that n|can−bn| < 2 for all nonnegative integers n.