IMO 1989 LL POR86
Given two natural numbers w and n, the tower of n w’s is the
IMO 1989 LL POR86
Origin: POR
Problem
Given two natural numbers w and n, the tower of n w’s is the natural number Tn(w) defined by Tn(w) = ww...w , with n w’s on the right side. More precisely, T1(w) = w and Tn+1(w) = wTn(w). For example, T3(2) = 222 = 16, T4(2) = 216 = 65536, and T2(3) = 33 = 27. Find the smallest tower of 3’s that exceeds the tower of 1989 2’s. In other words, find the smallest value of n such that Tn(3) > T1989(2). Justify your answer.