Let a,b be positive real numbers satisfying 2ab=a−b. Denote for any positive integer k xk and yk to be the closest integer to ak and bk, respectively (if there are two closest integers, choose the larger one). Prove that any positive integer n appears in the sequence (xk)k≥1 if and only if it appears at least three times in the sequence (yk)k≥1. number theory unsolvednumber theory