MathDB
Find the smallest integer m for which b_m > a_{100}.

Source:

September 15, 2010
number theorySequencesrecurrence relationInequalityIMO ShortlistIMO Longlist

Problem Statement

Consider the sequences (an),(bn)(a_n), (b_n) defined by a_1=3,   b_1=100 ,   a_{n+1}=3^{a_n} ,   b_{n+1}=100^{b_n} Find the smallest integer mm for which bm>a100.b_m > a_{100}.
Back to ProblemsView on AoPS