IMO Shortlist 1979 problem 19


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2. travnja 2012.
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Consider the sequences (a_n), (b_n) defined by
a_1=3, \quad b_1=100 , \quad a_{n+1}=3^{a_n} , \quad b_{n+1}=100^{b_n}
Find the smallest integer m for which b_m > a_{100}.
Izvor: Međunarodna matematička olimpijada, shortlist 1979