ILL 1979 Problem 54

Consider the sequences $(a_n), (b_n)$ defined by $a_1=3, b_1=100 , a_{n+1}=3^{a_n} , b_{n+1}=100^{b_n}$

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

Dataset text AoPS wiki problems. Quoted with source.

Solutions

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