1st Asian Pacific Mathematics Olympiad 1989 Problems

1st Asian Pacific Mathematics Olympiad 1989 ProblemsA1.  ai are positive reals. s = a1 + ... + an. Prove that for any integer n > 1 we have (1 + a1) ... (1 + an) < 1 + s + s2/2! + ... + sn/n! .A2.  Prove that 5n2 = 36a2 + 18b2 + 6c2 has no integer solutions except a = b = c = n = 0. A3.  ABC is a triangle. X lies on the segment AB so that AX/AB = 1/