49th Polish Mathematical Olympiad Problems 1998

49th Polish Mathematical Olympiad Problems 1998A1.  Find all solutions in positive integers to a + b + c = xyz, x + y + z = abc.A2.  Fn is the Fibonacci sequence F0 = F1 = 1, Fn+2 = Fn+1 + Fn. Find all pairs m > k ≥ 0 such that the sequence x0, x1, x2, ... defined by x0 = Fk/Fm and xn+1 = (2xn - 1)/(1 - xn) for xn ≠ 1, or 1 if xn = 1, contains the